I don't believe signal let's you import any of your old messages to new device's for security. When setting up a new device last time I saw a warning about this. It let's you use the same account but without the older messages.
You could try to copy your ~/.config/Signal folder to the same location on your new device but that might not work. Don't know because I've never tried.
Just tried it in Firefox for Android and it worked for me.
https://Lemmy.world !textiseopened up to
https://www.textise.net/showText.aspx?strURL=https%3A%2F%2Flemmy.world%2F