Welcome to the
kitz forum.
I can see that you actually have an NTE5/A and a Mk 3 SSFP installed.
Unfortunately the details of the wiring is not that clear, as you have taken those close-up photographs through the opening in the SSFP. If you look closely, you will see that there is a slot in the bottom edge of the SSFP which would allow it to be completely removed.
I believe there is more than one cable and some gel-crimps in the backing box behind the NTE5. So exactly how everything is connected together is currently a mystery.
With the lower front face-plate removed, you should find that your connection to the Internet should still be operational if you connect the modem/router to the top socket of the SSFP, as normal. Likewise, if you connect a telephone to the socket at the right of the SSFP, exposed with the lower fron face-plate removed, your telephony connection should still be operational.
That said, I believe your plan of action is sensible and should work. But I can't be absolutely sure . . .