Thunderbird, the Mozilla mail reader, comes with the ability to Forward an email (via an icon on the toolbar) which will send out the email under your name.
Sometimes it’s desirable to Redirect (or “bounce”) a message. Although it’s possible to detect that a message has been redirected, it looks very much like the original message with the same To, From, Subject, Date, etc., headers. In Thunderbird, this can be accomplished by downloading and installing a Thunderbird add-on.
The Mail Redirect add-on can be downloaded from: https://addons.mozilla.org/en-US/thunderbird/addon/550
After you install it (per the instructions on that page), you will probably want to add its icon to your toolbar (next to the Forward icon). Right click on the toolbar and select Customize… Drag the Redirect icon onto the toolbar where you would like it to be.
Now you can “bounce” a message simply by clicking on the Redirect icon.