Frames of multipliers in tensor products of Hilbert modules over pro-C*-algebras

Given a standard frame of multipliers {hn}n for a Hilbert A-module E and a standard frame of multipliers {tn}n for a Hilbert B-module F we construct a standard frame of multipliers for the external tensor product of E and F and for the inner tensor product of E and F using a non-degenerate pro-C*-morphism φ from A to the pro-C*-algebra of all adjointable module morphisms on F.