There is a small number of hedge traditions which have their own Magic Theory Abilities and, therefore, can make integration research. So, what happens if a member of one of these traditions (like the Folk Witches), make a full integration of a Virtue that grants a Supernatural Ability? Would it replace one of the tradition´s Favored Abilities? Or increase the total of Favored Abilities of the tradition by 1?
I would lean towards increasing the number of Favored Abilities by 1.
However you have to remember that not all Folk Witches have access to all of their Favored Abilities. So just because one Folk Witch managed to integrate a new Ability does not mean that all Folk Witches would have access to it. To get that access then they would have to be taught the change to Folk Witch Magic Theory by one who knew it.
The method of that teaching would be face to face for a Folk Witch, since they do not generally use text (most are not even literate). This would greatly slow its spread, likely resulting in a small specific tradition of Folk Witches who have access to an ability others do not. That is assuming it did not die off with the creator.
Most of the groups which have their own Magic Theory seem to be illiterate in fact. This is one of the big advantages the OoH has. Being able to produce a text which provides any who study it your breakthrough is important for providing a generally unified advancement of said Theory throughout all members of your Tradition.
keep in mind that most folk traditions do not use the favored abilities approach from Divine, infernal, and faerie, but instead have to initiate each of their virtues or open the whole lot of them at once as their own version of opening the Gift.
Note that the teaching in my first post was specifically talking about those with the Gift. Ungifted will always require being initiated into a new ability.
A "full integration" of an ability would only automatically be known when a new member of the Tradition had their Gift opened. For those already opened, being taught their version of Magic Theory for a season by someone who knew it would most likely suffice (YSMV). Comparing this to something just "integrated" which would always require an initiation to be taught.