In order to move a running process on your current shell to a new screen session, you can use reptyr and screen or even tmux.

Imagine that your connected via ssh to a remote server and your current job is taking to long to complete … or you forgot to open a tmux or a screen session and launch a long task …

I found the solution at serverfault, and an nice post at monkeypatch blog.

$ htop                 # Launch new process
$ ctrl+z               # Suspend the current process
$ screen               # Launch screen
$ reptyr $(pgrep htop) # Get back the process