To permanently save your progress and find your profile and your purchases if you change devices, it is indeed preferable to create your Fun account.
As long as you haven't done so, you will regularly receive invitations on your game screen to do so. If you want to do it on your own, you'll be asked to do so when you access the "My Account" menu.
At the time of creating your account, if you already have a Funbridge account, you can indicate that you already have an account. Then enter your Funbridge account information, by indicating in the "E-mail or nickname" field the e-mail address or the nickname you entered when creating your account.
You will also be able to do this if you are already used to identify yourself via a Facebook, Google, or Apple account.
If you are not in any of these situations, select the option "create a new account" and follow the instructions on the screen. Completing the registration will ask you to enter a valid e-mail address.