To top up the card, you’d need to register it & as far as I know, you can only register Monzo cards to a UK address (no doubt someone from Monzo will get back to you about this, after the holiday).
So…to put the transferring money issue in context, for anyone who’s still new to payments / Monzo - the cards are prepaid cards which means they’re designed to be used to make payments. The consumer bank accounts that are provided by the legacy banks can’t (please do point out any exceptions if there are some) accept payments, they can only accept transfers.
Obviously Monzo will be launching current accounts next year when they receive their full banking license. But…it’s safe to assume that Monzo would stil have to charge some fees (which is against their philosophy), in order to process payments which involve currency conversions.
The good news though, is that Tom has said that Monzo will be partnering with the provider of an FX solution which I assume, will enable Monzo users to transfer money abroad, without paying a huge fee. That’s all I know for now but more details should be announced at the same time as the current account launch.
Until then, I think you’re probably best off using another company’s services for this.