Item Familiar

[Deepwood Sniper]

Hello friends! I have a question related to item familiars. I'm allowing them in my campaign and as a random treasure, my players received a Headband of Intellect. the wizard of the group wanted to make it an item familiar. he upgraded it to a +6 (originally a +2). the question i have is: since an item familiar becomes an intelligent weapon with an Int, Wis, and Cha stat, would it also get the +6 increase to intelligence as well as the owner?

[Trundlebug]

No, constructs have their own intelligence score in addition to whatever other abilities they may have or impart.

EDIT: I suppose they may have an ability that lets them partake in their granted abilities but that would be homebrew.