By using Windows Live Hotmail's Contacts Options, export address book of your old account as a .CSV file and then import it to the new account from the same place, Windows Live Hotmail.
If your email address is non-Microsoft so cannot access Windows Live Hotmail's Contacts tab, try exporting and then importing them with
Windows Live Mail.
But to make sure importing action is done properly, you may have to empty address book of your new account first.
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