Make bread with flour different from the starter I have been able to cultivate a strong sourdough starter with whole wheat flour and  semolina flour.

Now I want to make a bread with all purpose flour, show should I proceed ?

Get this already active started and make my bread or feed it with flour until it gets used to ?
Your starter should have no problem working with other flours, you don't need to acclimatize it or anything. Just use it as you ordinarily would. 

I would suggest bread flour rather than AP, the higher gluten content will give better structure.