"Leaving" a connection open / Sessions

Greetings!

Is there a way to leave a connection open in SSH, something as a
'session' which can be restored later?

My scenario is the following: I connect to a remote machine (which has
sshd) via SSH, run octave, run a long script (which will probably take
about a month to complete), hit Ctrl+Z, type BG. So far so good, my
application goes to background.

What I would like to do next would be to log out of this ssh connection
and, when I return (with the same user), be able to fg %1 and return to
the running program. Right now when I try to do this I get a message
saying I can't, because there are jobs running on the background.

Is there a way to accomplish this? Some configuration in sshd perhaps?
I wouldn't like to have to leave two machines turned on whereas one
would suffice.

Thanking you for your attention,

Soleth

.

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