Yes, you may remain in the United States legally as long as your I-94 is valid

Yep, you’re good to stay for now! Even though your visa's expiring next month, what really matters while you're in the U.S. is your I-94

Yes, you’re still legal to stay. Your visa can expire, and that’s fine. Just don’t overstay that I-94. And if you leave the U.S., don’t forget—you’ll need a new visa to get back in