The UK Immigration Rules for Visitors state, in relevant part:
V 3.1 This Part applies to all applications for visit visas, leave to enter, and an extension of stay as a visitor except where explicitly stated otherwise.
(As a US citizen, you do not require a visit visa in advance; under the UK immigration rules you will apply for leave to enter by presenting your passport at the UK Border at the airport.)
V 3.4 An application (except for an application for an extension of stay as a visitor) will be refused if the applicant has been convicted of a criminal offence for which they have been sentenced to a period of imprisonment of:
(a) at least 4 years; or
(b) between 12 months and 4 years, unless at least 10 years have passed since the end of the sentence; or
(c) less than 12 months, unless at least 5 years has passed since the end of the sentence.
Where this paragraph applies, it will only be in exceptional circumstances that the public interest in maintaining refusal will be outweighed by compelling factors.
V 3.5 An application will normally be refused if:
(a) within the period of 12 months before the application is decided, the applicant has been convicted of or admitted an offence for which they received a non-custodial sentence or out of court disposal that is recorded on their criminal record (except for an application for an extension of stay as a visitor); or
(b) in the view of the Secretary of State the applicant’s offending has caused serious harm; or
(c) in the view of the Secretary of State the applicant is a persistent offender who shows a particular disregard for the law.
So, your friend should be fine to travel to the UK, if at least 12 months have passed since his probation ended.
Be aware, though, that:
- Your friend should be aware that when they visit the UK, they might be delayed at immigration for an extended interview. People can find this very stressful, but he should just try to relax and play it straight.
- Your friend should not attempt to conceal his criminal record at the UK border. There's no reason to do so, and lying to an immigration officer is also a great way to get refused entry.