Welcome to the forum
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Sorry to hear about your refusals
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1) Is it worth appealing? I haven't seen much on here about appeals. We believe that the ECO wrongly determined that my partner's employment doesn't qualify him as a sponsor, based on sections of the Appendix FM regulations that address how taxes are to be paid in just this situation. Therefore it's possible that a second look at our application by an ECO (which is the first step of the appeal process) could result in the decision being reversed and the visa granted for a mere 80 pounds.
No, I would not advise appealing.
For a start, it takes about a year for the appeals process, and it's unlikely to succeed unless you DID meet all the requirements AND you sent all the correct documents, but Sheffield overlooked them and made a mistake in refusing the visa... which they didn't.
Unfortunately, your UK partner must have guaranteed UK employment, by way of an official job offer with a UK company or have already started a UK job. Unless his current US company has UK offices and has approved a transfer, with an official letter confirming that he will be their UK employee, you cannot use his US employment for the visa.
2) Can anyone advise on what I should do to go to the UK as a US citizen on a visa waiver while we appeal? I'm planning to bring: 1) a letter from my employer stating my employment history and granting a leave of absence; 2) a letter from my partners' parents stating that I can stay there for the visit; 3) a lease in the US showing that my partner and I are maintaining a residence here; 4) return plane ticket.
There's no such thing as a visa waiver for the UK - that's a US program, not a UK one.
With 2 refusals for settlement visas already, I would not attempt to enter the UK without a visa.
You could try applying for a visitor visa, but I'm not sure it would be granted, firstly, because I'm not sure you can enter the UK while you have an appeal processing and secondly, because to enter as a visitor, you have to prove you have no intention of living in the UK... but you've just applied twice for a visa to move permanently to the UK.
To qualify for a visitor visa you need:
- evidence you will definitely leave the UK within 6 months and will not attempt to live in the UK
- enough money to support yourself without working for the length of the visit
- very strong ties to the US to prove your life is there and you will not attempt to live in the UK, such as:
i) a US job to return to (you have been given time off by your employer)
ii) a home you are maintaining in the US
iii) family members in the US you need to return to
iv) other commitments in the US you must go back to, such as weddings, events, interviews, appointments, college enrollment etc.