Connecting an exterior outlet to an interior outlet
The question I would have is the box large enough to have 7 conductors and a device for wire fill calculations. I would turn the power off remove the wires from the back stabs and connect the 2 existing blacks with the new black and a short pig tail to the inside outlet. once that is done I would do the same to the Hot side making sure to keep the polarity correct to the outlet. Tie the ground for the new outlet to the existing grounds. With that done install a GFCI outlet outside with a "in use" or extra duty cover and it would be fine. Make sure to use the same gauge wire to the new outlet (you can use larger but that affects the box fill calculations. With 14 awg wire 18 cu inch box would be needed (if plastic no clamps +2 if it has clamps) for 12 awg wire 20.25 cu inch box would be needed if no clamps (+2.25 for clamps).