When you cancel a nonrefundable ticket, you get credit in the amount of the cost of that ticket towards a future flight minus the $150 fee. The credit is valid as long as it is applied towards a new booking within one year.
When I did this, I was never mailed a voucher. Instead, the info stayed in their system and when I called to apply it towards a new ticket, they were able to locate the credit by my AAdvantage Number. But a PNR or an Eticket number would also work.
In order to apply the credit towards a new booking, the easiset thing to do is to get your reservation on AA.com, place it on hold, and then call AA with you new reservation number and they will complete the booking for you and apply the credit towards towards the price of the ticket. Or, you could just book the entire thing by phone.