I have a Time Warner Cable mailbox.  Quick test shows that a reply using TWC webmail does not quote richtext (HTML) content.  This indicates that your Pegasus Mail user friend is sending only richtext content (he is not including a plain text version).  The option in Pegasus Mail that controls this is located at Tools > Options > Outgoing mail > Sending mail > "Generate multipart/alternative versions of richtext messages".

I suggest he check that setting, enable it if it isn't, then send you a test message, perhaps one that he sent previously that was problematic.

OTOH, if this setting is already check then we need to continue looking elsewhere.

Time Warner Cable Webmail user ... cannot REPLY-TO ... Pegasus Mail user ...

 Patience with me please ... I have tried to address this with TWC with little luck.

 When I do Reply-To:   which normally inserts some "quoting characters" along with original message into my email client (which happened to be a web client by TWC).  

 This all works for all my email sending buddies ... except the Pegasus mail user ... whose messages are coming through as "text/html" even though fairly plain.   

 How can I debug this problem ?  Is it some bizarre character in the email ? 

Are you saying that the Pegasus Mail user sees a plain text version rather than a fancy (also called HTML or Rich Text) version?  If they are receiving a content type of "text/html" then I suspect they have Pegasus Mail configured to view messages in plain text by default.  Clicking the "View" icon in the message reader or pressing Ctrl+v will toggle between plain text and fancy view when both formats exist in the message.  Also, the attachments tab of the message viewer window will list any alternate message formats.  If both formats exist, "plain text" and "HTML text" will be listed.  If you confirm they are receiving the HTML content then they can either use the toggle options as described above or configure Pegasus Mail to display the fancy version when it exists.

I'm a Time Warner Cable webmail user.  I don't use Pegasus  Mail. My friend uses Pegasus Mail.

He does not see a problem. I see a problem when I do reply-to:   when I do that for his messages ... the WebMail processor cannot grab the message and put in the quoting charaters for me.   The copied message buffer is nearly blank. 

 I'm really just trying to find someone who might know more about email processing that I do. And I'm still at least suspicious that the problem  starts with how his Pegasus mail sends out his emails.  

[quote user="ggaliens"] I'm really just trying to find someone who might know more about email processing that I do. And I'm still at least suspicious that the problem  starts with how his Pegasus mail sends out his emails.   [/quote]

Possibly a charset decoding issue: Can you access the headers of such a message and post them here (after removing all adresses or other personal details, of course)?