A pet door that fits the PetSafe pet door hole size.
This is a friction-fit design and shouldn't need any glue or fasteners to keep it in the wall or door. I suggest sanding the inner edge of the outer part (if making a different depth) to help make inserting the insert easier.
I also included a longer-than-needed version of the outer part so that you can easily slice it to whatever depth you need (the default size fits a 130mm wall depth.)
Slice to: Desired Depth + 4
Update:
I added a friction-fit cover that I made to close off the pet door. The image is attached (it is a white cover).