@Sita4
It might be the best and quickest way to simply ask your guest to compensate you directly. Especially since they texted you the photo and (hopefully) admitted being responsible. These are the key issues here, and claiming from Airbnb (with or without a security deposit) is a time consuming exercise that does not always work out. And you must claim within 24hrs of the guest departing, and also history shows that guests get less likely to feel responsible or pay for damages as time passes - so you must move quickly.
Airbnb will likely want to see original install invoices for the cabinets, as well as have a professional & registered company (not a handyman) give their estimate for repair..... as well as written admittance from the guest. And it is possible that your reply to the guest text of taking care of it after check-out may go against you (not meaning to be difficult here - just saying).
So if you think you can, just chalk this one up to learning and quickly get in touch with the guest and ask for a contribution towards repair. He can pay through the resolution center and do this BEFORE your review. Just think of a reasonable amount (it won't be enough of course - but something is better than nothing) and request it. Soon. Most people, if they feel responsible for some damage, will pay up to $100 directly without it becoming a long and drawn out exercise.
I know it seems disappointing that Airbnb don't offer to reimburse for anything and everything that gets damaged, broken or stolen - but let's be realistic here - that would be impossible andeven our own household insurance companies don't do this (not many policies offer accidental damage new for old replacement without charging hefty additional premiums...) - and when there is an Airbnb 'insurance' claim on the host guarantee - very strict guidelines are followed and most aren't successful (rightly or wrongly - just stating the facts).
I hope you are able to sort something and please do let us know what you do and any results - it will help another reader/host with their own situation one day.
Best Wishes.