  In this note we extend the methods developed by Freidel et al.
[arXiv:hep-th/0612170] to derive the form of $\phi^4$ interaction term in the
case of scalar field theory on $\kappa$-Minkowski space, defined in terms of
star product. We present explicit expressions for the $\kappa$-Minkowski star
product. Having obtained the the interaction term we use the resulting deformed
conservation rules to investigate if they lead to any threshold anomaly, and we
find that in the leading order they do not, as expected.
