Would you like an 'official' answer to your subsidiary question, or a 'real life' one? I'll offer both:
Under the provisions of Section 1182 of the (US) Immigration and Nationality Act, "any alien convicted of, or who admits having committed, or who admits committing acts which constitute the essential elements of . . . a crime involving moral turpitude" is ineligible to enter the USA. (There are exceptions relating to offences by minors and to offences which can't result in imprisonment for more than one year, but they're not relevant here).
Theft counts as 'moral turpitude'. Accepting an FPN constitutes an admission of guilt. So (doing things 'by the book') your partner can't travel under the Visa Waiver Program or (in the first instance) obtain a visa to enter the USA. He's meant to submit a visa application to the US embassy, together with a document from the Association of Chief Police Officers detailing his 'record'. He'll then have to attend an interview at the US embassy in London, only to be told that the matter has to be referred to Washington to find out whether a 'waiver of ineligibility' can be granted. The waiting time for an interview is about 4 weeks. The waiting time for a response from Washington is usually about 13 weeks (but sometimes much longer) . The processing time after that (if a visa is granted) is a further 4 weeks.
That's the 'official' answer. The 'real life' one is that the US immigration authorities have no direct access to UK police records. If your partner simply 'forgets' about his brush with the law, and enters the USA under the Visa Waiver Program (with an ESTA) there should be no problems.
Chris