That would be a hard no from me. But I’ve been a landlord before - for 5 years . I have zero desire to do that again.
Absolutely not! I agree with everyone who says Airbnb is not the place for this kind of rental. If you want to rent to someone for four months (which I never would), get a a rental agreement or a lease, as has been said. This request doesn’t look right to me and I’d have second thoughts about even a week under these circumstances.
This week I got a similar request from a woman who was house hunting. They are selling in 3-5 days. This means that her actual dates could be variable by as much as a month either way.
She has no reviews. Yes, I declined.