Can a green card holder sponsor a divorced spouse for a green card?

Yes—if you were married while you were a permanent resident and the divorce occurs after you filed I-130 and it was approved, they may still proceed under “spouse” rules if the divorce was involuntary

Generally, after divorce, the “spouse” relationship ends; the derivative benefit is lost unless you can show battery or extreme cruelty under VAWA provision

If the divorce is final before filing or before approval, the I-130 must be withdrawn; they’d need another qualifying sponsor.