Wrap your sum in Assuming[Element[l, Integers], expr], for example:
Assuming[
Element[l, Integers],
Sum[{A[l, l1, i, j, k, l]/B[j, j + 1, i, j]} KroneckerDelta[i, l], {i, 0, \[Infinity]}]
] //InputForm
(* {Piecewise[{{A[l, l1, l, j, k, l]/B[j, 1 + j, l, j], l >= 0}}, 0]} *)
