Water damage from neighbor, best way to claim insurance?

[Lawrence Hsu]

Hi

Newbie here. Have a rental in a condo building in Los Angeles. Tenant occupied. A unit above left their water on, causes damage to my unit below. They have already admitted fault, and I have an email stating that. Damage probably a few thousand dollars, mainly that the walls need to opened and dried to prevent mold. Already have someone working on it now to mitigate damage at this point, Is it best to claim this through my own insurance, then have them go after the party at fault? Or, should I claim with the insurance of the party at fault?

My main concerns

1. Being made whole with the least hassle

2. Not having this count as a claim that I filed, which would raise my future premiums

Thanks in advance for any advice!