I changed my smartphone. What do I need to do to make sure Cycloop works?

You simply have to download the Monimoto app on your new phone and log in using the same log in method which you used when you first created your account:

Sign-in with Phone  (this requires you to have access to the phone number you used when you first created your account due to SMS short code verification)
Sign-in with Google
Sign-in with Apple

Make sure you use the same method as your original Sign-in otherwise it will create a separate account.  Each Sign-in method creates separate accounts from each other.