There is nothing to transfer. Your subscription belongs to the store account you bought it with — your Apple ID or your Google account — not to a particular phone.
A new phone, same kind of phone
iPhone to iPhone, or Android to Android: sign in to the store as usual on the new phone, install Cupla and sign in to the same Cupla account. Your subscription is already yours and comes with you.
Switching between iPhone and Android
This is the one case where a subscription cannot come with you. Apple and Google each hold their own purchases, and neither can hand one to the other.
Your current subscription keeps working until the end of the period you have already paid for, on whichever store you bought it from. After that you can subscribe again on your new phone's store.
Two things worth knowing before you decide:
Subscribing on the new store while the old subscription is still running means paying for both at once. Nothing links them.
Cancelling does not refund what you have already paid. See How do I request a refund?
Cupla Premium follows your account, not the store
Premium is unlocked for the Cupla account you sign in to. That is why an iPhone subscription still gives you and your partner Premium when you sign in to the same Cupla account on an Android phone — the purchase stays with Apple, but the access travels with your account.
It is also why one subscription covers you both: Cupla charges once per couple, not per person.
Premium is missing on my new phone
Almost always this means the new phone is signed in to a different Cupla account rather than your original one — a new, empty account looks exactly like a subscription that did not come across. Please do not subscribe again: it will not bring your data back, and you would be paying twice.
See How do I set up a new phone?, or message our support team from the Cupla app and we will put it right for you.