From Company Trips, search for (e.g. HELiO booking #, trip name) and select the trip you want to transfer to your account.
Select Settings from the left navigation menu, click the Options icon to the right of the Trip name and dates, and select Transfer Trip.
When prompted to transfer this Trip to your user, select Transfer and wait for the "Success" message.
The Trip will now appear under My Trips on your Dashboard.