I was wondering if tighten our belts would give a hero resource if that hero moves his resource to another hero? Example: I move a resource from Denethor to Boromir and i don't use his resources for anything else. During refresh phase i use tighten our belts which gives Denethor one resource since he didn't actually spend any resources. Correct?

If the effect you used to move those resources says " move X resources to another hero's pool," then yes. If it says " spend X resources to add that many resources to a hero's resource pool," then I'd say no. Hope that helps.

Denethor don't spend a resource to make a hero gain, he only move. I know that because I was playing the noldor allies who gain 1 defense each time a hero gain a resource from a card effect, and Denethor never help it :(.

Yes it will work. And if you spend one or two resources on Boromir, Boromir won't receive any resource but Denethor will gain a resource, because the game don't track who originally own the resource, it only check if the hero have or not spend a resource this turn.