Answer: has begun
The teacher already has begun the lesson.
Step-by-step explanation:
The sentence seems to be missing a verb, which has to be chosen out of the provided options. Given that the subject is the teacher, the proper conjugation should be made with the pronoun 'he'. If the verb was conjugated in the past, it should be 'he began', while in Past perfect it would be 'he had begun', but neither of those options is provided.
Therefore, we can only assume that the verb is conjugated in the Present perfect, so the correct answer is 'he has begun'.