Can a Godparent be in an invalid marriage?

Can a Catholic in an invalid marriage be a Godparent ?

Depends on what you mean by that. If someone is presumed validly married but later on divorces and obtains an annulment that states the marriage was never valid, it does not retroactively revoke their Godparent status.

However if someone is currently in a marriage that is not recognized as valid by the Church then they cannot be a Godparent because they cannot fulfill the responsibilities of being a Godparent:

Can. 872 …A sponsor also helps the baptized person to lead a Christian life in keeping with baptism and to fulfill faithfully the obligations inherent in it.

Can. 874 §1 To be permitted to take on the function of sponsor a person must:

3/ be a Catholic who has been confirmed and has already received the most holy sacrament of the Eucharist and who leads a life of faith in keeping with the function to be taken on;

If someone is in an invalid marriage he is not fulfilling the obligations of his own baptism and therefore cannot be considered for the role of helping another person to fulfill his Christian obligations.

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