Both of them is correct but there is difference between them.
In "The boy accompanied his Mum" this is the boy that accompanied her mother. The boy is subject and his mom is object.
In "he was accompanied by his Mum" his mom is subject and that boy is object. this type of sentence is called "the passive voice" that object is more important than the subject.
More example:
1- The man clean the room _ The room is cleaned. As you see in the first part, subject is "the man" and mentioned who cleans the room but in the second part "the room" is important and it doesn't matter who cleans the room.