from our reference frame safely outside the black hole, all the objects that fall into it never make it through the event horizon: they appear to get stuck there in a vanishingly thin layer just outside the EH. This includes electrical charges, which to us appear to reside on the EH and radiate their field lines outward into space just as if the black hole itself (inside the EH) was charged. So any net electric field that a black hole may possess is simply the sum of all the charge that fell onto its event horizon over its lifetime, plus whatever charge it originally had before it collapsed into a black hole. 

Those charges radiate their field into space and would be detectable to us in the same way any other charged object would be.