@Anonymous User
Yes, it will be five months after the three-month Pass started before you are asked to pay any more money to continue the service.
However, the two-months Pass from the Stick, if it was applied electronically, will appear as a voucher in the area at the top of your My Account/Passes & Vouchers display, and will require you to Redeem it.
Which you can only do when there is less than one month to go on your existing 3-month Pass, so you can’t do it yet.
But as soon as you are in the third month of your current Pass, then go into that area at the top of Passes & Vouchers, and Redeem your two-month Voucher, which will then kick in automatically as soon as the three-month one ends.
If you forget, and don’t Redeem it in time, then you will be charged for the fourth month, but the voucher will still be there to be Redeemed, and will cover the fifth and sixth months instead when you Redeem it, so you will still get your free two months one way or the other.
If you had a paper Voucher with your Stick (unlikely now), then the rules are very much as above, except you will be Redeeming the paper Voucher at the appointed time instead of one stored on your account. And you will have to look after the paper Voucher, and not lose it in the meantime 
