Thanks to all who helped. I've learned something new. The most important is
RJ45 is not the same as 8P8C even though they look identical. RJ45 is for
networking and 8P8C is for phone. There are 4 twisted pairs
RJ45: (4, 5) (3, 6) (1, 2) (7, 8)
8P8C: (4, 5) (3, 6) (2, 7) (1, 8)
For noise free phone operation, it is probably better to find out whether
the jacks are RJ45 or 8P8C so the 4 phone lines travel in 4 twisted pairs in
the network cable.
Someone has suggested this item which splits a RJ45 connection into two
2-line phone jacks:
This looks exactly like what I need, assuming the jack in the wall is wired
as RJ45 (mostly probably).