the form of the twist and the corresponding relation between the twist and the $R$-matrix.

In this paper we elucidate and solve the above problems in a different approach, using deformation of the Heisenberg algebra and coalgebra by twist. In Section 2 we introduce the undeformed Heisenberg algebra and construct the corresponding coalgebra. We also present a type of tensor exchange identities and show that the introduced coalgebra is compatible with them. These identities appear to be crucial in our construction. In Section 3 we deform the Heisenberg algebra and coalgebra by the twist deformation and get the deformed tensor exchange identities that are also compatible with the deformed coalgebra structure. This deformed Heisenberg algebra includes the $\kappa$-Minkowski spacetime. By using the homomorphism of the coproduct and the introduced tensor exchange identities, in Section 4, continuing analysis from Ref.[@Kovacevic:2012an], we give the coproducts for the Poincaré generators, proposing two new methods of calculation, which are explicitly illusrated in few examples. In Section 5 we give the exact form of the universal $R$-matrix, generally for the deformed Heisenberg coalgebra and especially for the $\kappa$-Poincaré Hopf algebra, and present the method by which it can be cast into a form including Poincaré 