I was stuck in a large mv so I wasn't in a position to stop the process, setup screen and then start it again. I managed to exit the SSH session with the process running by essentially doing the following steps:
Establish SSH connection: ssh user@host
Run the desired command to start the process
Press Ctrl+Z to pause the process
Run bg to put the paused process in the background and resume it.
Run disown [pid] (process ID is optional, defaults to last process) to disown the process. To get a list of jobs simply type jobs before.
Exit the SSH session by running logout.
Usage of the disown command:
disown [-ar] [-h] [jobspec ... | pid ... ]
Without options, remove each jobspec from the table of active
jobs. If jobspec is not present, and neither the -a nor the -r
option is supplied, the current job is used. If the -h option
is given, each jobspec is not removed from the table, but is
marked so that SIGHUP is not sent to the job if the shell
receives a SIGHUP. If no jobspec is supplied, the -a option
means to remove or mark all jobs; the -r option without a job?
spec argument restricts operation to running jobs. The return
value is 0 unless a jobspec does not specify a valid job.