Uhhhh, well as long as they didn't have a "bad" break up I think it's okay to message and ask how she's doing?
Usually I'd tell my friends it's not a good idea if they came from a really bad relationship
where there was some sort of abuse or unreconcilable difference they angrily fought over.
But from how the guy described his ex, it was about having kids and I think and stuff like that can change over time,
so I think it's okay to just message to check up since it wasn't anything deeper to the break up like something physical/psychological
while I'm not sure if they should get back together immediately, I think it's okay to start back at square one where they try to learn who they are as a person now.