Moving an already-running process to Screen

Have a look at reptyr, which does exactly that. The github page has all the information.

reptyr – A tool for “re-ptying” programs.

reptyr is a utility for taking an
existing running program and attaching
it to a new terminal. Started a
long-running process over ssh, but
have to leave and don’t want to
interrupt it? Just start a screen, use
reptyr to grab it, and then kill the
ssh session and head on home.

USAGE

reptyr PID

“reptyr PID” will grab the process
with id PID and attach it to your
current terminal.

After attaching, the process will take
input from and write output to the new
terminal, including ^C and ^Z.
(Unfortunately, if you background it,
you will still have to run “bg” or
“fg” in the old terminal. This is
likely impossible to fix in a
reasonable way without patching your
shell.)