Thanks. Meantime, I have found (and today bought) an adapter made for this purpose. (See http://www.mikescomputershop.com/extender-over-cat5e-cat6-connection-150ft-p-21441.html).
So far it, works if I use a long ethernet (CAT5E) cable between the printer & router, but it doesn't work via the ethernet wall plugs that use the telephone lines.
So maybe that means the telephone lines aren't shielded (?). Another reason it might not be working is because the max. cable length it works for is 150 feet & I don't know what the routing is through the walls along the existing telephone lines that were originally installed just for telephone.
I'll keep exploring to see if I come up with either a solution or an answer. Any other suggestions would be welcome.