On the utility of Robinson-Amitsur ultrafilters. II

We extend the result of arXiv:0911.5414 about embedding of ideal-determined algebraic systems into ultraproducts, to arbitrary algebraic systems, and to ultraproducts over $\kappa$-complete ultrafilters. We also discuss the scope of applicability of this result, and correct a mistake from the previous paper concerning homomorphisms from ultraproducts.