[Giangibar]

First of all, I'm pointing out that the bidding is very far from natural (this board was played in the context of Moscito: an artificial system with weak and transfer opening bids) and it could have some consequences on the play.
In first seat, all red, you pick up ♠KQxx ♥xx ♦AJ87x ♣xx and decide to follow your system by opening 1♥ = 4+♠, could be canape, 9-14 points. LHO doubles, partner passes (showing tolerance for playing in Hearts), RHO passes too. You could just pass and sit in 1♥X, but you decide to follow the system and bid 2♦ = 4♠ and 5♦, minimum. LHO passes, partner passes (showing preference for Diamonds over Spades) and RHO bids 3♣. You pass, LHO bids 3NT, partner quickly doubles and the bidding ends. Partner leads the 4 of Diamonds (attitude, showing 1+ honors in Diamonds but no indication about suit length) and dummy comes on the table with ♠xx ♥xxx ♦10x ♣KQ109xx. Declarer seems disappointed and calls for a small Diamond. What do you play? The Jack, hoping to maintain communication with your partner in your likely running suit but risking to give declarer a free trick, or the Ace, winning the trick and preventing declarer from getting a trick he could be not entitled to, but maybe severing communications with partner?

[Free]

I'd play the Jack.

The Jack has other advantages: if you'd play ♦A and continue ♦, declarer might be able to block the suit (K9x in his hand). When the suit is blocked, he can comfortably play any finesse your way and succeed. And if he'd want to develop a ♠ trick (AJTx or something similar), he can because your entry would be gone too soon.

PS: in the editor there's a button with the ♠ symbol. It's a hand editor, which makes such problems much easier to read.