The names of those confirmed with mention made of the minister, the parents and sponsors, and the place and date of the conferral of confirmation are to be recorded in the confirmation register of the diocesan curia or, where the conference of bishops or the diocesan bishop has prescribed it, in a register kept in the parish archive. The pastor must inform the pastor of the place of baptism about the conferral of confirmation so that a notation is made in the baptismal register according to the norm of can. 535, §2.
Source: Code of Canon Law (Vatican.va)