The conservator’s authority over your mother’s assets ended upon your mother’s death. The conservator will still have to file a final accounting with the court.
Your mother may or may not have had assets which need to be probated. Any assets held jointly or had a beneficiary named to be paid after her death (life insurance is a good example) will avoid probate and pass directly to the new owner. Any assets which your mother owned in her own name will need to go through probate.
Depending on the values of the probate assets and where your mother resided when she died, she may or may not qualify for a small estate probate, sometimes called a voluntary, which does not have all the requirements of a full blown probate and is open for a shorter period of time.
In order for you to have access to the probate assets, you will need to present a petition, the last will and testament, and a death certificate to the probate court. I suggest that you speak with a probate attorney to walk you through these requirements. A full blown probate is a long, drawn out cumbersome process with deadlines and filing requirements.