Evicting a Tenant in Texas

I am buying a full duplex in Texas, with a closing date set for May 20. The seller is filing for an eviction of one of the tenants, who was already given notice to vacate because he was on a month-to-month lease, and subsequently failed to make this month's rental payment. Even if the seller is able to get a judgement against the tenant before our closing date, if he does not move out voluntarily afterwards, I suspect she can't get a writ of posession to force him out before May 20.

If I close on the house with the tenant in residence after the current seller gets a judgement against him, can I continue the eviction that was already started by the seller and get a writ of posession? Or do I need to start over and get a new judgement against him?