All you need to do is login to the same Monimoto account you already have existing. To do that make sure you login using the same details as your original account, choose either login with email, sign in with apple (for iOS devices using Apple ID) or use login with phone number.
You do not need to re-pair the Monimoto device to your new phone via Bluetooth or any other way if your Monimoto account already has the device paired, all you need to do is login to your account.
If you have forgotten your account details you can check them on your old phone by going to top-right corner person icon (account settings) which can be found here. There you can see if email or phone is your primary account type, then you can login using either phone number based on the primary info on your new phone.