I came across this:
"Early versions of the Compaq Portable 386 were sold with the Compaq Portable III case and badges. A differing screen bezel stating "386/20" was the only externally visible change."
so i would assume he has an early Compaq Portable 386 which is still marked as a Portable III (originally a 286 system)
also found a picture of the inside of a Portable 386 ('upgraded' to a 486) which took those '42 pin simms' here: (they appear to be what he needs)
http://www.386page.com/systems/Compaq/portable-386/portable386.php
as well as the maintenance and service manual here:
http://www.manualslib.com/manual/273076/Compaq-Compaq-386.html