Context
I am a British citizen and for a little while have been collecting antique (section 58) firearms in the UK. I will shortly be marrying my American fiancée and emigrating to the USA to do so, applying for permanent resident status (Green Card).
I have been selling my collection in the UK to British citizens to try and get rid of it before I emigrate. I am not a registered business, I am a private collector who buys and sells in small amounts (approx. £600 annually).
I know UK firearms law for sales within the UK well. I Have read the antique definitions in US law and know my items are antiques in both countries, (although as both countries have poorly-informed customs and law enforcement, it is always useful to know what would happen if antiquity was disputed). I do not know any US law about international sales inside other countries such as registration or citizenship.
Intention
I will be leaving the antique guns with my parents in the UK (who will continue to treat them as curios/ornaments under section 58). The guns would remain advertised on a UK website for UK sales only. They would be boxed and wrapped and my parents would arrange a courier or royal mail them (my parents will not require any UK license to transfer antiques as a curio or ornament).
Said guns would not be leaving the UK because then I might need a USA Export License. (I know the reverse is true - if I stood in the UK causing guns to leave the USA and go to anywhere else - for example, there was an RFD dealer prosecuted for negotiating a gun sale exported from China to Nigeria, without having a UK Export License)
Requests
Is there any US or UK law which stops me continuing to advertise my guns for sale on a UK website, in the UK, within the UK, to UK citizens?
Additionally, I wish to know: If they were NOT antique guns, what US requirements would I need to be negotiating UK-UK sales while living in the USA? I am aware I would need to be an RFD or have other certification as a UK citizen, I ask regarding US law. (If there is any dispute as to antique status, it would be useful to know if, for example, the USA don't care if they're AK47s as long as they don't touch the US border.)
Many thanks in advance
(I understand answers and comments cannot be taken as true legal advice, however, any specific legislation sections or legal cases that you can point me to I can then read for myself.)