You should allow an option to have live.com email to be forwarded to another email.
Allow a setting in live.com email to be forwarded to another email address
Thank you for reaching out to us. We don’t support this through outlook.com on the mobile browser. But you can set up a forwarding rule from your live account if you go to outlook.com from a laptop or a desktop. Just go to Settings → Mail → Forwarding.
Let us know if this helps.