screen
command (ex: vi /tmp/file)
CTRL+a d # which is 'CTRL' and 'a' at the same time, and then 'd'. This will 'd'etach from the screen session, while screen itself still runs! (and inside it the commands, shell and any still running invoked command, still run)

#log in the original machine (host A) as the same user ORIGINALUSER, and then:
screen -r   #will reattach to the latest running screen from that user.