He committed a misdemeanor in America and was sentenced to three months' imprisonment by the judge. Can he go to America after returning home?

You didn't describe the incident in detail, but said a general crime, which is hard to say.

However, anyone who goes to prison, enters the court, etc. , can no longer be exempted.

Therefore, to sum up, it is more difficult for you to get a visa and immigration approval.

Unless your case is passive. For example, A hits you and you hit C, which leads to C's death. You're in prison. This situation is passive, and you can appeal for exemption.