UKtoUSA2020

He is a green card holder as of 2020-12-31 so he will qualify for all 2020 stimulus as long as he as SSN.

When did he get his GC? If it was in 2020 you don't need the statement electing him to be treated as a resident for the whole year.
 
Apart from that, yes he qualifies for all the stimulus checks.

Thanks everyone. Sorry, I just realised I hadn't replied!
 
We've decided to use Petair UK - primarily because of the lack of other options right now and uncertainty with covid. It's a lot more than we thought we'd be spending, but are so happy we found a way to take our cat with us.

Ive taken both (2)dogs and cats from the UK to the USA. You can do everything yourself and do not need to use a courier, who will charge you a ton more money than it needs to cost.
There is an export certificate for live animals that you should get from DEFRA. It is a simple process but just needs to be sorted in advance.
As per all travel, ensure your pet is in good health well in advance and make sure all the vaccinations are up to date. As was mentioned earlier in the thread, look up the respective state requirements for bringing pets in to that state. Make sure you have a 'fit for travel' vet certificate for your pets prior to traveling. Worth ensuring the vet is open and has an appointment space for the check well in advance to suit your travel plans.
Be mindful of temperature restrictions ie the time of year, as some airports do not allow pets during the hottest and coldest months. Cats are normally permitted inside the cabin if you wish.
It is wise to have your pets vaccinated against rabies if they have not been already as this is pretty much a standard requirement for most states.
 
I have found in the main, that when you arrive at the POA, customs typically are not interested in the pets, but are more worried if you have brought any food for them with you. 
 
Bottom line is if you check the requirements and the airline policies prior to booking, it doesn't need to be expensive or troublesome to take your pets. Lufthansa are the best airline to travel with from my experience when it comes to bringing animals.
 
Good luck and kudos to you for keeping your pets with you.
 

I used PetAirUK (https://www.petairuk.com/) to fly my dog over last autumn. It wasn't cheap, and they definitely tried to upsell an airport liaison service we didn't need, but the process was pretty smooth.
 
I did not need a Pet Passport (I thought that was just for EU travel), but did need his vaccinations up to date and a rabies shot (not strictly required but they advised it might avoid any hold ups in customs). They handled the vet paperwork declaring him fit to travel and checked him in at the airport.

We are using petair uk to ship our cats, so they do all the liaising with airline/airport and we don’t need a pet passport. Like Gaz1a says, these are for bringing your pet back into UK and with Brexit that system will be replaced at the end of the year. 
 
We are taking our two cats to the vet in an hour to get their rabies jab. However, we were told they technically don’t need it (we’re moving to Georgia) but we thought it would be better safe than sorry. 
 
 
 
 

I moved my two cats to the US last year and can’t recommend https://airpets.com more highly!! 
They collected my cats from York and drove them to Heathrow, had them all checked out and certified by their vets before they left. I provided them with my paperwork from my vet. Flew them to Dallas, made sure they were settled for a day or so then drove them to me in Oklahoma. 
You will need the cats to have had rabies jabs at least 30 days before they travel and your vet will know anything else the cat needs, mine needed up to date flu shots.
 
air pets were amazing, my kitties are happy Okey cats now and I wouldn’t have survived here without them!
 
a note of caution if your cat does not meet entry requirements then they  don’t allow them in and don’t send them back. 

Hey, 
 
So my wife just flew to US with our dog. She's an American citizen so they've gone ahead while I wait for my visa 😕.
 
Ok so this will be for a dog but it may be useful.
Pet passports are only valid until end of this year and will no longer be valid as new systems will come into play following Brexit. They are not cheap - about £150 I think - we got one because when we did, we thought (before COVID) we may come back to the UK beforehand. You do not need a pet passport to leave the UK. You do not need to liaise with Heathrow Animal Services or Animal Reception Centre (they only deal with inbound animal travel). There is no fee except if you pay for a service. Check the state - each US state has different requirements - California (for us) only required all the standard dog vaccines plus Rabies so we did that - if you haven't got it already - you should do it up to 3 months before travel. Again may be different for a cat My wife was able to secure an 'emotional support animal' request from our GP - it means your pet can travel with you in the cabin. Every airline that flies direct to the US will allow an 'emotional support animal' in the cabin. BA were amazing about it when we contacted them. There is no fee, the animal just has to not be over a specific size and weight. There is obviously the other option of cargo if you want.  Heathrow Airport staff did not have a clue what was going on. They literally didn't know. It was very funny. My wife told me that security just loved seeing an animal and when she got on the plane (this was June) there was hardly anyone on the flight so the cabin crew loved having a dog onboard. There are a multiple number of services that do all this for you where they take the pet the day before and you meet the animal and a representative when you touch down in the US. 
 
Hope this helps. Let me know if you have any more questions!