According to Generator rule a model gains power field rule. Power field beside preventing 5 dmg per focus allows to heal 1 dmg per focus.
Can warjack also heal dmg?
If yes does it need a non crippled generator or head systems to do so?
Yes, any model with the Power Field rule can spend 1 focus to heal damage. That’s literally part of the rule. 
And, yes, it may be unintentional that Generator does not also prevent healing damage while crippled. For an answer of intent and an official ruling, we’ll need @elswickchuck to weigh in.
As worded yes it works
As for intention…I’ll have to check
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