Both sentences are grammatically correct, but they have slightly different meanings. I have changed the 'he' in the example sentence to John to help eliminate confusion in my answer:
A) John said that he will continue the research as soon as he returns.
means that at the time the author wrote the statement, John has definitely not yet returned, but when he does, he will continue the research (at least, that's what John said he would do). The only time this would be correct grammar, is if the author is certain that at the time of writing the statement, John has still not yet returned. If John has definitely returned, or even if its possible that he has returned, then it would be more correct to say:
B) John said that he would continue the research as soon as he returned.
This is a much less specific statement in terms of time, and allows for the situation that John has already returned, that he hasn't yet returned, or that he may have returned without the author's knowledge at the time the author writes the sentence. If John has returned, then presumably he is either continuing the research already, or he has broken his word.