My mother is running a recent version of MS-Outlook and has a POP3
email account from her ISP.  I have set a redirecting SLD up for her that
forwards email to her ISP email account.  How can I set her
Outlook so that outgoing email appears to have come from the
forwarding domain instead?

I don't know about Outlook, but I just checked Outlook Express. With
OE, if you go to the account Properties, you can place the e-mail
address on the General tab. Whatever you put there is what will show
up in the From line.

This is somewhat unlikely, but some larger ISPs have their SMTP
servers set to not allow the sending of email that does not have their
domain in the From: field.

Tools>account>Properties>Reply address
Reply address as the one from the isp.

Good afternoon,
Excuse me I answered too quickly...
But here is the answer:
You have to change adresses in Outlook using the menu
Tools>account>Mail>Properties>
You are now seeing your ISP's mail properties.

Replace Email address and Reply address by the one you want to
appear(the previous you had you forwarded).
Change only this part and it will be ok.