The theories don't correspond. They have nothing to do with each other. Introvert Rationals typing PiJe and Introvert Irrationals typing JiPe means jack squat because MBTI does not recognize the Static/Dynamic dichotomy.
MBTT does not consider functions as static/dynamic, there is a whole different window typology and types are being viewed from than in Socionics.
To paint a picture:
There is a soda machine in the U.S. that takes U.S. dollars. A guy has paper money from another country that can fit in the US dollar slot. The guy slides it in and it's half-received by the machine, but then gets rejected because his paper money and the US Dollar are made of different substances even though they seem the same on the surface.
The U.S. Dollar is Static/Dynamic, the foreign paper money is P(e)/J(e).
It doesn't matter what types people get typed as. A person is always what they are. The fact that Socionics calls that person Static, or MBTI calls them JePi is irrelevant. If you know the structure of MBTI you would see that it cannot logically coexist with Socionics, especially in where Rationality/Irrationality is concerned. Either one of them is wrong & one is right, or they are both wrong.