Why do Catholics accept a Lutheran baptism?

Dear Catholic Answers!

As an infant I was baptized a Lutheran (newer a practicing Christian), at 21 converted to Mormonism, and now at the age of 41 I’m finally coming home to the Catholic church – in parts because of the wonderful work you guys are doing!!!
I’m in RCIA at the moment and when baptism was discussed I was surprised to learn, that because of the Lutheran baptism I received as an infant, I’m not required to go through the sacrament of baptism now as an adult convert. It was something I have looked forward to fore a long time, so to be honest I’m a bit disappointed at that and, as I said, surprised.
In Mormonism, as I’m sure you know, the right to baptize is closely associated with the priesthood. It is in other words the authority to act in the name of God. To Mormons this right was restored to Joseph Smith and Oliver Cowdery in may of 1829.
In Catholicism we talk of Apostolic succession were the authority of the Apostles, which they received from Christ, was given to the Bishops of the church, and that that authority has persisted in the church down through the ages.
In the reformation north the church in Germany and Scandinavia broke with Rome and the Holy See and set up national churches built upon the ideas of Luther. They are, as fare as know, not recognized by Rome as having apostolic authority.
Why is it then that the Catholic church recognizes the Lutheran baptism that I have received? My own guess is that I because of my Mormon background have misunderstood, among other things, what priestly authority really is.

Sincerely!
Frank Jensen.

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