If the father had a will, the will probably needs to be admitted to probate to obtain letters testamentary (official acknowledgement that a designated person can act on behalf of the estate). The executor, appointed in State X, can then proceed to have an ancillary probate proceeding in State Y (i.e., to get officially recognized in that state). This might be necessary if the oil interests are deemed real property (if not as an intangible asset authorization in state X, would suffice). Once these ancillary letters (again, authorization to act on behalf of the estate in State Y) is obtained, this person would have the appropriate documentation and authority to transfer title (ownership) to mom. While it might sound daunting, many jurisdictions have special simplified proceedings for small estates.

The lesson for others to learn from this is the importance of addressing ownership/title to assets. If the ownership were owned in a trust or as joint tenants, the above steps might not have been necessary.

Caution: the rules and proceedures differ signficantly from state to state. The terminology and even steps above might be wrong. Your best bet is to consult with an experienced probate attorney in State X as a starter. If you need an attorney in State Y, your State X attorney or the company might be able to make recommendations.