How to copy files between two computers using SSH

You could use scp:

When you're on PCB:

scp -r your_user_name@ip_address_of_PCA:/path/to/remote/directory /path/to/local/directory

On PC A, instead of connecting to PC B by ssh, just run

rsync /path/to/local/file username@PCB:/path/to/remote/destination

You could also use scp instead of rsync, with similar formatting for the rest of the line, but I prefer rsync, since it's more powerful, and (I think) verifies after copying. See man rsync for more details. N.B. that the remote computer must have rsync installed too (see comments by neon_overload), otherwise scp would be preferred.

If installed on both computers, rsync will take advantage of the processing power of both. For example, it can compress files before transfer, by using the -z flag.