Plantinga defines strong actualization thus: "God strongly actualizes a state of affairs S if and only if he causes S to be actual and causes to be actual every contingent state of affairs S* such that S includes S*" (Profiles, p. 49).
It is crucial for Plantinga's arguments that "includes" have an interpretation such that if S entails S* and S* is contingent, then S includes S*. Otherwise, Plantinga's FWD includes an invalid argument. For Plantinga is going to argue that if W is a world where Eve freely doesn't take the apple, then T(W)--the maximal strongly actualized state of affairs that includes all the states of affairs strongly actualized in W--does not include Eve's freely refraining from taking the apple, and hence the conditional T(W)→(Eve freely refrains from taking the apple) cannot be necessarily true. But the latter only follows if entailment implies inclusion.
Moreover, it is crucial to the FWD that God cannot strongly actualize a state of affairs of someone doing something freely.
But now we have a problem. For suppose that in some world W where Eve freely doesn't take the apple, God earlier confidentially remarks to the Archangel Gabriel that if Eve doesn't freely refrain, God will create life on Pluto. Let S1 be the state of affairs of God making that remark to Gabriel, and let S2 be the state of affairs of there being no life on Pluto. Suppose S2, as well as S1, obtains at W. It seems that God strongly actualizes S1 and that God strongly actualizes S2.
But now we have a problem, for God strongly actualizes each of two states of affairs whose conjunction entails Eve's freely refaining. Now it either is or is not true that if God strongly actualizes each of two states of affairs, he strongly actualizes their conjunction. If it is true, then it follows, contrary to what is needed for the FWD, that God strongly actualizes Eve's freely refraining. If it is not true, then T(W) need not in general exist--there will, perhaps, always be a state of affairs that includes all the states of affairs strongly actualized at W, but that state of affairs will not itself be strongly actualized by God (why? becuase that state of affairs will include S1 and will include S2, but the conjunction of S1 and S2 is not strongly actualized). And Plantinga's argument seems to require the existence of T(W).
Probably the best move in response would be to say that although God causes S1, he doesn't cause all the entailed states of affairs, and hence he does strongly actualize S1. One of the entailed states of affairs is the disjunctive state of affairs: (Eve freely refraining and God's telling Gabriel that Eve will freely refrain) or (someone other than God telling Gabriel that Eve will freely refrain). To cause a disjunctive state of affairs God would, it seems, have to cause one of the disjuncts. He does not cause the second disjunct, as it does not obtain, and he does not cause the first disjunct, because then he'd be causing Eve to freely refrain, which is impossible (according to Plantinga). Therefore, God does not strongly actualize S1.
This response has one problem: Plantinga cannot afford to say that by causing a disjunctive state of affairs God has to cause one of the disjuncts. For, surely, God causes Eve to freely take or freely refrain from taking, but God does not cause either disjunct.