Windows Live Mail program and Hotmail account - sent items are not saved

["Mortimer" <me@xxxxxxxxxxx>]

A customer is using Windows Live Mail as a replacement for Outlook Express 
to send/receive mail for a Hotmail account: this was forced upon him because 
Hotmail have withdrawn support for the protocol that OE uses for accessing 
web-based mail such as Hotmail.

Despite a Tools | Options | Send setting "Save mail to Sent Items" being 
enabled, no sent mail gets saved to that folder. I can't find anything about 
this symptom in Live Mail's help or on support.microsoft.com. Has anyone 
encountered and fixed the problem?

Interestingly, the customer also has a POP account that he monitors with 
Live Mail, and (usually) sent items which are sent from that account do end 
up in its Sent Items folder.