Homestead Exemption question

[Huy Thai]

PROPERTY TAX QUESTION: If I'm buying a home that has homestead exemption with two months left in the year as an investment property, do I get to benefit from the homestead discount for the 2 months that I'm paying for 2019? Seller contribution for 10 months is based on the discounted amount with exemption. What I don't want is for the tax man to come asking for the full amount (non exempt) come Jan 1 which would mean I'd have to fork up an additional $600 for months that I didn't own the home. 

I guess my question simplified is once it's designated, does the Homestead last the whole year even if the property changes hands?

[Marci Mayes]

I have purchased quite a few rental properties in Texas over the years. My experience has been that the exemptions in place on the property on Jan 1 stay with the property for the remainder of the year. For example -- If I purchase a rental with a Homestead exemption, Over 65 exemption, etc, I benefit from the exemption the first year. This gives me time to stabilize the property by doing repairs, finding tenants, etc. before the property tax exemption falls off the next year.