If I understood the question correctly, you want to move a multisite sub-site from one site to another multisite subsite in different domain or server?
There is a plugin that can do this easily: https://wordpress.org/plugins/prime-mover/
The plugin can also do: single-site to single-site, single-site to multisite, multisite to single-site and multisite subsite to another multisite subsite migrations (just like your case). Just activate on the network admin go to the sub-site listed in Network Sites and click Export to generate site package. On the target end.
One thing that is important is that in WordPress multisite, subsite is identified by blog ID. So it means that if in the origin multisite, the subsite has a blog ID of 7. It needs to be migrated also on the target server with a blog ID of 7.
Otherwise if its different blog ID, it could mean different site. So cannot mix it up.
Ideally in multisite to multisite migration, domain name / website URL can change. But not its blog ID, which is supposed to be used as a means of identification.