AppleScript: How to un-hide the file extension of a screenshot?
You were close! You need to use file in front of (filePath as POSIX file), e.g.:

set filePath to "/Users/Me/Desktop/" &amp; "Screenshot" &amp; ".png"

do shell script "screencapture -mx -T1 " &amp; filePath

tell application "Finder"
    set extension hidden of file (filePath as POSIX file) to false
end tell