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Re:Reptyr – Reparent a running program to a new terminal by caipre on Sunday December 07, 2014 @06:09PM (#8713991)
screen (and tmux) start a new instance of the shell, which would have no knowledge of the backgrounded process. You'd just see the message "fg: no current job"
Re:Reptyr – Reparent a running program to a new terminal by emmelaich on Sunday December 07, 2014 @11:12PM (#8714881)
And even if you could(1), the background process typically has the terminal open - and screen uses a separate pseudo terminal aka pty -- As suggested by the name - rePTYr

(1) ^Z sends SIGSTOP; to continue you can signal SIGCONT. But then what?!