If I understand the question correctly, you're wondering if you can/must play Missile Envy for your last AR? The answer is yes, you must play Missile Envy for ops.
You're also probably obligated to thank your opponent for being so nice. =P
EDIT: Interestingly, if you had a HELD card, you would have to give that to your opponent. So you would start the last AR with a scoring card and Missile Envy. In that case, you could play the scoring card, but would be obligated to play Missile Envy for Ops on AR1 of the next turn. You can never be obligated to hold a scoring card. (Someone can correct me if I'm wrong here, but I'm pretty sure there was a thread on this exact scenario).
EDIT2: 10.1.5 A player may not be forced to Hold a Scoring Card through the effects of an Event(s).