I wanted to move with Signal to my new Fairphone4 WITH all chats.
Here is how I made it!
First of all:
Download the newest version of signal (NOT from any store!):
Signal >> Signal Android APK
Create a data backup from your old smartphone, do NOT forget to note alle the numbers (pass key)!
Copy the data backup from your old to you new phone
Insert your SIM-Card into your new phone, you will need it to activate it.
Start Signal and choose to restore Signal with your local backup
(if this does NOT work, you don`t have the newest Signal Version. You can not use the Signal Version from /e (too old version))
You will need to enter your Signal Code and you will get 1 SMS with a veryfy code, type it
(Hope this will help others saving time)