I've always been able to transfer history, from Android phone to Android phone, when I switched to iOS, I didn't bother since my wife was just going to start using Messages due to its encrypted nature. I really only used Signal with my wife, she only used it because I was using it and it allowed us to send images back and forth without losing quality.

> without losing quality

Signal does lossy compression on images. You can change image quality from “Standard“ to “High“ in its settings but not disable it.