Inheritance after receiving Medicaid

My father inherited a good amount of money while he was living in a Nursing Home and receiving Medicaid. However, the inheritance was received only a few months prior to his death.

Is Medicaid eligible to take the entire inheritance or just the portion that Medicaid paid for the cost of the nursing home from the time the inheritance came in until the day he passed?

I also heard something about a "threshold" this inheritance could be without Medicaid coming after it. I have done some research and cannot find anything about this "threshold."

Does anyone know what the "rules" are for inheritance after someone is in a nursing home and on Medicaid? And is anyone familiar with this "threshold?"

Thank you.