The renter is someone she knows and has been paying her rent to live there. There is no formal lease. Does that make a difference?
I would say it isn't necessary, but if you had a lease agreement, it may help. We have seen many tenants purchase short sales and it has not been a problem. On the same note though many banks will complete a buyer verification internally to audit the buyer. If the bank finds a reason for concern with the buyer ( family, potential financial benefits to the borrower ) they would not allow them to purchase the property.
Ask the lender.