Concerning the woman’s prior marriage, if her husband is still alive then an annulment investigation (by the tribunal of a Catholic diocese) would be required. If the tribunal determines that the marriage was invalid (from a sacramental standpoint) then she would be considered free to get married to someone else, including a Catholic man.
If the husband from her prior marriage has passed away then an annulment investigation is not needed because marriage vows are only binding until the death of a spouse.
I recommend that the Catholic man meet with a priest or deacon in his parish to discern what the next step in the process would be.
