I did it before since I've had this app for years now but I couldn't remember how. Since there's no root access, I can't copy the backup file from and into the sandbox.
I've been unsuccessful at sending myself an e-mail via the backup feature so I resorted to using my favorite file manager to save the file to a directory I had access to. I then copied the file to my computer to be copied back to the new phone.
On the new phone, make sure the file has the right extension, which mine didn't. It has to be *.hlptrz
Then on the new phone you can tap on this file, open it with Laptimer, and the app will do the rest.
