I googled it for you and found this: https://serverfault.com/questions/24425/can-i-nohup-screen-an-already-started-process
It doesn't create a file, but you don't need one. Read all the answers for options on reattaching. I haven't used it, so I can't vouch for any of them. (Personally I just use byobu and have it start with each shell, so I'm always running tmux.)
I don't think there's any system that can reliably freeze a single process to disk. Usually that's implemented by the program itself.