Jedi Exile and Extra Attack with Ambush

Just to clarify an interaction here. Thanks.

If the Jedi Exile gives Extra Attack to a Savage character (through Empathy) with Ambush, can that character use the extra attack after moving? For example, can a Rakghoul get four attacks against an enemy who has not activated if it stays within 6 squares of the Jedi Exile?

I know the extra attack says the character can't move, but the Ambush ability says you can move and still attack multiple times. Just want to clarify if the Extra Attack from Exile works just like Triple Attack already on the character's card.

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The Jedi Exile's CE: [Allies within 6 squares gain Extra Attack.]

Extra Attack: [On its turn, this character can make an extra attack, but it can't move if it does so. This works just like other special abilities that grant extra attacks, such as Double Attack. This extra attack stacks with those granted by other special abilities and commander effects, and it also stacks with Extra Attacks granted by different special abilities (so the same ally could receive multiple extra attacks in the same turn).]

Ambush: [On its turn, this character can move and then make all of its attacks against a single enemy who has not activated this round. Many abilities that grant extra attacks, such as Triple Attack, require the character not to move, but Ambush lets it move and make extra attacks as long as all are against the same enemy.]
I would want to say yes since ambush says make make all attacks, (its effects simular to Greater Mobile just that you can't move 2 then 4 or whatever)
Yes.