Move a file to external disk and remove the original

Question

This is a script that was supplied to me on these forums it has been working well, but all the transferring of the files took place locally so a 'Move' command does it eactly what it says, however I now need to move it to an external drive, as a result it leaves trace of the original file.
How can I make it MOVE and remove the origial File please?
set fileMatrix to {¬
          {folderName:"BHS", prefixes:{"BH70", "SM70", "AL70", "BH11"}}, ¬
          {folderName:"Bu", prefixes:{"BU40", "BU11"}}, ¬
          {folderName:"Ca", prefixes:{"CW"}}, ¬
          {folderName:"Da", prefixes:{"ES20", "AM20"}}, ¬
          {folderName:"Di", prefixes:{"DV25", "DV11"}}, ¬
          {folderName:"Do", prefixes:{"DJ30", "RA30", "DJ11"}}, ¬
          {folderName:"In", prefixes:{"GT55", "CC55"}}, ¬
          {folderName:"Fr", prefixes:{"FR10", "FR11", "FR17"}}, ¬
          {folderName:"No", prefixes:{"TM17", "NN_"}}, ¬
          {folderName:"Ma", prefixes:{"MA65", "MF65", "FI65", "MC65", "MH65", "MB65"}}, ¬
          {folderName:"Pr", prefixes:{"PR_"}}, ¬
          {folderName:"To", prefixes:{"TM15", "TM11"}}, ¬
          {folderName:"Wa", prefixes:{"WA35", "WA11"}}, ¬
          {folderName:"Se", prefixes:{"SE_"}}, ¬
          {folderName:"Mik", prefixes:{""}}}
tell application "Finder"
  --set theHotFolder to ((path to pictures folder) as text) & "HotFolderDone"
          set theHotFolder to folder "StudioA:Users:StudioA:Pictures:HotFolderDone"
  --set foldericon to ((path to pictures folder) as text) & "Icons:Rejected Folder Done"
          set foldericon to folder "StudioA:Users:StudioA:Pictures:Icons:Rejected Folder Done"
  --set fakeTrash to ((path to home folder) as text) & "FakeTrash"
          set fakeTrash to folder "StudioA:Users:StudioA:FakeTrash"
set a to alias "Scratches:Workings"
          repeat with matrixItem in fileMatrix -- look for folder
set destinationFolder to (folders of a whose name starts with folderName of matrixItem)
                    if destinationFolder is not {} then -- found one
                              set destinationFolder to first item of destinationFolder -- only one destination
                              set theFolderName to name of destinationFolder
                              repeat with aPrefix in prefixes of matrixItem -- look for files
                                        repeat with startFile in ((files of theHotFolder whose name starts with aPrefix) as alias list) -- move files
                                                  try
  move startFile to destinationFolder
                                                  on error
  activate
                                                            display dialog "File “" & (name of startFile) & "” already exists in folder “" & theFolderName & "”. Do you want to replace it?" buttons {"Don't replace", "Replace"} default button 2 with icon 1
                                                            if (button returned of the result) is "Replace" then
                                                                      set {fileName, t_ext} to {name, name extension} of startFile
                                                                      if exists file fileName of fakeTrash then -- and it also exists in the fakeTrash Folder.
                                                                                set name of file fileName of destinationFolder to "this is a unique name" -- or whatever
                                                                                set newName to my getUniqueName(fileName, t_ext, fakeTrash)
                                                                                set movedFile to move file "this is a unique name" of destinationFolder to fakeTrash
                                                                                set name of movedFile to newName
                                                                      else -- not exists in the fakeTrash Folder.
  move file fileName of destinationFolder to fakeTrash
                                                                      end if
  move startFile to destinationFolder
                                                            else -- "Don't replace"
                                                                      if not (exists folder "StudioA:Users:StudioA:Desktop:Rejected Folder Done") then
                                                                                set theLastFolder to duplicate foldericon to desktop
                                                                      else
                                                                                set theLastFolder to folder "StudioA:Users:StudioA:Desktop:Rejected Folder Done"
                                                                      end if
                                                                      delay 0.5
  move startFile to theLastFolder with replacing
                                                            end if
                                                  end try
                                        end repeat
                              end repeat
                    end if
          end repeat
          try
                    if (count theLastFolder) is 0 then delete theLastFolder
          end try
end tell
to getUniqueName(theName, theExtension, someFolder)
     check if someFile exists in someFolder, creating a new unique file name (if needed) by adding a suffix
          parameters -          theName, theExtension : a file name and his name extension
                              someFolder : a folder (finder item or alias)
          returns :     a unique name
          set {counter, suffixes, divider} to {0, "abcdefghijklmnopqrstuvwxyz", "_"}
          if theExtension is not "" then set theExtension to "." & theExtension
          set theName to text 1 thru -((length of theExtension) + 1) of theName -- just the name part
          set newName to theName & theExtension
          tell application "Finder" to set theseNames to name of items of someFolder
          repeat while theseNames contains newName
                    set counter to counter + 1 -- hopefully there aren't more than 26 duplicates (numbers are easier)
                    set newName to theName & divider & (item counter of suffixes) & theExtension
          end repeat
          return newName
end getUniqueName

Answer 1

I do not have the time to read through your whole script and give specific answers, but the general principle is fairly easy.  You're moving with the Finder, so your move command is going to be of the form:
tell application "Finder"
  move file xxxx to folder yyyy
end tell
For cross file system moves (which are as you point out actually duplications) just add a line after each move that sends the old file to the trash:
tell application "Finder"
  move file xxxx to folder yyyy
  delete file xxxx
end tell
the Finder has an empty trash command that you can use at the end of the script if you like.
One gotcha: because move has two different behaviors, the second code block will throw an error if you try to use if for a local move (it will move the file properly, then try to delete the file it moved, which is obviously no longer there).  For clarity, I'd use duplicate rather than move for if you're working across file systems.  That's what you're actually doing, and if you use the move command you may confuse yourself when you come back to look at the script a year down the road.