Water-Damaged Faced Insulatiion - but before install. Can I use it?
I would just cut out the bad part and tape the two pieces together  that would give you much more even insulation than trying to patch and keep the existing kraft face. If the bat is not long enough for the wall cavity the kraft face should be taped to prevent excessive air movement anyway. The kraft face should almost always go towards the interior. If right along the coast there may be a few exceptions. Make sure there is no mold still in the insulation before installing.