Additional info to supplement my question:
For the past couple weeks emails directed to our primary address are read on the laptop which is on a home wireless network and located at the other end of the house. When I access the OE6 account on the desktop the emails are not found.
I carefully checked the entries for the mail account on both computers and am assured the data for both email accounts is the same.
Prior to this recent problem the messages appeared on both computers and a return to that condition is desired since the laptop is used only during the periods we have the nearby TV operating; the desktop is supposed to be the primary.