I was installing a new storm door to the front of the house this weekend and found the bottom five inches of the doorjamb is rotted (where the closer bracket needed to be screwed onto) (see photo). The king and jack studs are also rotted away behind the jamb, from the sill plate up 5-6 inches.
I'm concerned about structural integrity as the king and jack studs not intact from top plate to the sill. I've attached a photo of the jamb where I've screwed in a piece of sheet metal until I can get it repaired properly. Behind the metal plate is the rotten area (about the width of a stud and extends in at least 6-8 inches horizontally and down a few inches to the sill.
My question: Should the king and jack studs be replaced from the sill to the top plate or can I use something like a scarf joint to repair them once I've gained access to them?