**Abstract**

The aim of the paper is to study modules for the twisted Heisenberg-Virasoro algebra at level zero as modules for the -algebra by using construction from [*J. Pure Appl. Algebra* **219**(2015), 4322-4342, arXiv:1405.1707]. We prove that the irreducible highest weight -module is irreducible as -module if and only if it has a typical highest weight. Finally, we construct a screening operator acting on the Heisenberg-Virasoro vertex algebra whose kernel is exactly vertex algebra.

**Key words:** Heisenberg-Virasoro Lie algebra; vertex algebra; algebra; screening-operators.

**Dražen Adamović and Gordan Radobolja, SIGMA 12 (2016), 113, 13 pages; arXiv:1605.08608; http://dx.doi.org/10.3842/SIGMA.2016.113**