I am having an endogenous variable X1 and an exogenous variable X2 and instruments Z1 and Z2 for my endogenous variable and having one interaction term between endogenous and exogenous variable X1*X2. So my model goes like this

Y = X1 + X1* X2 + controls

I used instruments Z1 and Z2 in the first stage regression and then use the fitted values of X1 from my first stage to use in the interaction term X1*X2
in the second stage. Have I done this correctly?