On the prime ends extension of unclosed inverse mappings

We consider mappings that distort the modulus of families of paths in the opposite direction in the manner of Poletsky's inequality. Here we study the case when the mappings are not closed, in particular, they do not preserve the boundary of the domain under the mapping. Under certain conditions, we obtain results on the continuous boundary extension of such mappings in the sense of prime ends. In addition, we obtain corresponding results on the equicontinuity of families of such mappings in terms of prime ends.