Don't worry about his age. Those ages are just a guide because brand new parents have no idea what 13kg means - saying "This will last around 12-15 months" is just a guide. The car seat is safe as long as he is under the max weight and his head isn't over the edge. Actually many children can fit into infant carriers up to 18 months, even 2 years and beyond.
I would put him in it now, pull him down in the seat as far as he will go, see how close his head is to the edge of it. If you only have a cm or two, then I probably wouldn't chance it - in 3 months' time, he may well be too tall. If you have more than an inch of space, then he will likely be fine (but do check again 2-3 weeks before you travel).
You are generally allowed to gate check two items of baby equipment for free, that includes a car seat. If you take your Cybex in its original box (if you have it) it would be safe/protected. It would be a pain, but use a luggage trolley and check it in immediately and it might seem a bit more doable.
Otherwise, the options are:
- Buy a seat for the next stage you can use on the plane (you would need to book him his own seat).
- Buy a seat online to be delivered to your relatives, so they don't have to pay. Or buy one here and immediately forward it onto them in the same box. Car seats are incredibly cheap in the UK compared to other European countries.
- Hire a seat from a baby equipment hire company/ERF specialist.
- See if your relatives can borrow a seat from a friend, or find an expat network nearby where someone may lend you a seat.
Further notes:
1 - Officially the only two approved ones are Diono Radian 5 (which can be rear facing) and Britax Eclipse (which is only forward facing). But European airlines are funny about car seats in the first place. Generally for an under 2 with their own seat, you MUST use a car seat for them, but for older children sometimes you'll be refused use of a seat even if it's supposed to be a flight approved one. Some airlines have the policy that you can use any seat, as long as it can be fitted forward facing and will fit on the airline seat - standard airline seats are 46cm wide IIRC. So it needs to be narrower than this. Infant seats generally always fit and most of them are flight approved. Joie Juva is an inexpensive one which is quite tall in height, if you can try him in one in a store before you go. Obviously it might feel a waste to buy a seat just for one trip though. I would also look at Joie Tilt, Joie Steadi and Britax Two Way Elite. All of these would be able to rear face at your destination. Another option might be Britax First Class Plus. It is only rear facing to 13kg but by the time of your next trip, he will be older.
2 - I am already up way too late but if you want to do this and want someone to help you browse Portuguese online shops for suitable car seats I would be up for that.
3 - Klippan (ERF specialist up to 25kg) are a popular brand in Spain and run a system where they hire seats out to tourists/occasional drivers wanting to ERF. I don't know whether this system extends into Portugal. You do have to leave a hefty deposit which might freak out your DH! Mine was actually OK with it, which surprised me. You could email them and ask (I sent a crappy Google translated to Spanish email and got a helpful response back! They are actually Finnish, so you could just ask in English if you email Klippan direct.) Especially if your relatives live near the Spanish border, they might be near a shop that offers this. Otherwise, there are several organisations which hire baby equipment out to tourists generally based near airports. The quality of the items might be questionable and you might have to clarify which exact model of seat you'd be getting to ensure it's rear facing, but it's an option, and some of them do have decent seats like Maxi Cosi Pearl (rear facing), Britax etc. Obviously, the issue with hiring anything is ensuring that it's an appropriate model, up to date and not been mistreated. I would guess (?) that a baby equipment type hire place would be better at this than a car hire place (which tend to have horror stories) - but I don't know. It depends who is running it.
4 - May have the same issues in getting hold of an ERF seat and/or a seat which hasn't been mistreated.