Sharkey and Firefish both offer this, tho they handle it a bit differently. Those two are "built in" and the idea is that the imported posts don't federate, they just get imported with you. You would lose favorites, boosts, and in most cases, reply history. Sharkey states they are able to import replies as well for Mastodon and Twitter, but I haven't seen it in action yet (just came out this week).
Firefish - Import from other firefish instances, mastodon. I don't know for sure, but I assume IceShrimp has this as well.
I tried Firefish, and it did work for my very small collection of posts from another instance.
Sharkey - Import from Misskey/Firefish, Mastodon/Pleroma/Akkoma, Twitter, Instagram, Facebook. Sharkey states that for the Mastodon flavors and Twitter, replies to your posts are also imported (?) Not sure how that works.
If you have some technical background, there's another option, Mastodon Content Mover tho it does "spam" your posts, so be sure to use this BEFORE you import or add followers. Just like the other options, replies, likes, boosts, etc. aren't included. It's written in Java.