This works with folders if the nesting only goes one level deep.

If you may have multiple levels of nested folders, it could be modified to be recursive.

Applescript:

# folders on different devices
set path2source to choose folder with prompt "Select the source folder" default location (path to desktop)
set path2dest to choose folder with prompt "Select the destination folder" default location (path to desktop)
set path2list to choose file with prompt "Select your textList" of type {"txt"}

set theList to paragraphs of (read path2list)

tell application "System Events"
   set theFiles to path of files of path2source
   set theFolders to every folder of path2source
   repeat with aFolder in theFolders
       set theFiles to theFiles & (the path of files of aFolder)
   end repeat
   set sourceList to {}
   repeat with aFile in theFiles
       if (name of disk item aFile) is in theList then
           set end of sourceList to my quotedIt(aFile)
       end if
   end repeat
end tell

do shell script "mv " & my recolle(sourceList, space) & space & quoted form of POSIX path of path2dest

#=====

on quotedIt(aFile)
   return quoted form of POSIX path of aFile
end quotedIt

#=====

on recolle(l, d)
   local oTIDs, t
   set {oTIDs, AppleScript's text item delimiters} to {AppleScript's text item delimiters, d}
   set t to l as text
   set AppleScript's text item delimiters to oTIDs
   return t
end recolle

#=====

Try this:

Applescript:

# folders on different devices
set path2source to choose folder with prompt "Select the source folder" default location (path to desktop)
set path2dest to choose folder with prompt "Select the destination folder" default location (path to desktop)
set path2list to choose file with prompt "Select your textList" of type {"txt"}


set theList to paragraphs of (read path2list)
global theFiles
set theFiles to {}

tell application "System Events"
   my addSubfolderItems(path2source)
   set sourceList to {}
   repeat with aFile in theFiles
       if (name of disk item aFile) is in theList then
           set end of sourceList to my quotedIt(aFile)
       end if
   end repeat
end tell

do shell script "mv " & my recolle(sourceList, space) & space & quoted form of POSIX path of path2dest


#=====

on addSubfolderItems(aFolder)
   tell application "System Events"
       set theFiles to theFiles & (the path of files of aFolder)
       set theFolders to the folders of aFolder
   end tell
   repeat with someFolder in theFolders
       addSubfolderItems(someFolder)
   end repeat
end addSubfolderItems

on quotedIt(aFile)
   return quoted form of POSIX path of aFile
end quotedIt

#=====

on recolle(l, d)
   local oTIDs, t
   set {oTIDs, AppleScript's text item delimiters} to {AppleScript's text item delimiters, d}
   set t to l as text
   set AppleScript's text item delimiters to oTIDs
   return t
end recolle

#=====

I don't write recursive handlers much, and so far when I do I've just been using global variables to avoid having to handle information passing through the levels of recursion.

Just for the heck of it, I thought I should figure out how to do this without a global variable. Here's that copy, in case it's of use to you. The end result should be identical.

Applescript:

# folders on different devices
set path2source to choose folder with prompt "Select the source folder" default location (path to desktop)
set path2dest to choose folder with prompt "Select the destination folder" default location (path to desktop)
set path2list to choose file with prompt "Select your textList" of type {"txt"}


set theList to paragraphs of (read path2list)
set theFiles to {}

tell application "System Events"
   set theFiles to my addSubfolderItems(path2source, theFiles)
   set sourceList to {}
   repeat with aFile in theFiles
       if (name of disk item aFile) is in theList then
           set end of sourceList to my quotedIt(aFile)
       end if
   end repeat
end tell

do shell script "mv " & my recolle(sourceList, space) & space & quoted form of POSIX path of path2dest


#=====

on addSubfolderItems(aFolder, theFiles)
   tell application "System Events"
       set theFiles to theFiles & (the path of files of aFolder)
       set theFolders to the folders of aFolder
   end tell
   repeat with someFolder in theFolders
       set theFiles to addSubfolderItems(someFolder, theFiles)
   end repeat
   return theFiles
end addSubfolderItems

on quotedIt(aFile)
   return quoted form of POSIX path of aFile
end quotedIt

#=====

on recolle(l, d)
   local oTIDs, t
   set {oTIDs, AppleScript's text item delimiters} to {AppleScript's text item delimiters, d}
   set t to l as text
   set AppleScript's text item delimiters to oTIDs
   return t
end recolle

#=====