Can this sentence be translated also as "This is his letter."? If not, then what would a Vietnamese translation look like?
The meaning is the same, but it would back translate to "Đây là thư của anh ấy."
Your suggested translation is correct. However, this type of sentences are to teach learners about possessive pronouns. In this case, "thư" is the subject, "của anh ấy" is the possessive pronoun. Though the English sentence sounds unusual, this form (something is someone's) is common in Vietnamese conversation.