What you can do is at least match the members in each group.
That should give who is in both groups
The above should give those group members who liked a specific page.
The feature needs to be rolled out to the group you would like to join as well as the page you would like to join.
(I don't believe it's 100% rolled out to everyone)
In addition, the admin must enable it in the group settings.
Once, that's done, you should be given the option.
No, Facebook does not archive the posts but for your purposes they may as well be archived.
Facebook uses infinite paging. In order to see older posts you have to page down and down and down until your browser cache sucks up all your available memory and crashes your computer.
Buy more memory and a weight to put on the page down key
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