I like to transfer the incoming e-mails from my hotmail inbox to external e-mail addresses and leave the original e-mail in my hotmail inbox.

Currently Windows Live hotmail does not allow this.
In the "Forward mail to another e-mail account" we can set  up only MS e-mail boxes and the forwarded messages will be deleted from the inbox.

Is there any solution?

Regards

Pal

I don't know of an official Office Live solution to this.

Thre's the following restriction "You can forward your mail to one other e-mail address that ends in hotmail.com, msn.com, live.com, or is part of Windows Live Custom Domains"

You can use 3rd-party service, like http://forwardlive.com

Strange -- Under Options --> Forward mail to another e-mail account I can set up any account I want and am currently forwarding it to an external Exchange server that I use to consolidate several accounts. Works great...