I recommend asking a priest to evaluate your grandmother right away. (If you believe that she is near death, there is no reason to wait for your priest-friend to return from overseas. A local Catholic priest can take care of this situation now.) If your grandmother has the ability to reason and wants to be received into the Church, a priest can help you do what is necessary to receive her into the Church immediately. She can receive conditional baptism, confession (if she’s able), confirmation, first Communion, and the anointing of the sick.
If your grandmother does not have the ability to reason – as your report indicates by her belief that she already is Catholic – but if she expressed a desire to join the Church before she lost the ability to reason, she can be received into the Church. Ask the priest about this. If she did not express such a desire previously but if you do not know whether she has been baptized and if she expresses a reasoned desire for baptism, she can be conditionally baptized. If she is in immediate danger of death and there is no time to call a priest, you can conditionally baptize her yourself. The formula for conditional baptism is “If you are not already baptized, I baptize you in the name of the Father, and of the Son, and of the Holy Spirit.”
If your grandmother cannot express a reasoned desire for baptism or to enter the Church, then you are going to have to entrust her to the mercy of God, knowing that he will not spurn anyone who loves him and desires to be with him. (See the article linked below for an explanation of the Church’s teaching about salvation outside the Church.) To help her prepare for death even in her diminished capacity, you might say to your grandmother in one of her more lucid moments, “When Jesus comes, Grandma, say ‘I love you.’”
Can Outsiders Be Insiders? by Fr. Peter Stravinskas