Transfer deed of deseased relative

I saw this question a lot but my situation is kind of unique. My grandfather passed away 2 years ago in June. He had insurance on the house which paid off his mortgage due to accidental death. The only will we found was from 1969 which was before his birth daughter was born however he mentions my mother in the will but he never legally adopted her so the military never recognized her as his daughter so that left my aunt able to handle all of his final affairs. My mother was told by my aunt that the property was going into both their names but my mom never signed any kind of paperwork to transfer the deed. I have been living in the house the past year and a half and my question is if my mom pays the taxes owed on the house can she have the house put in her name? I did a search on the property and records show it is still in his name and the tax information is still in his name. The property is in florida.