This question is based on a question https://mathoverflow.net/questions/177678/when-is-the-restriction-h2g-mathbbc-to-h2k-mathbbc-surjective
I am asking this as a new question as I already asked that user but got no response.

I wish to know what is that algorithm by which I can check that a 2-cocycle on $K$ is image of 2-cocycle on some some subgroup of $G$ under the restriction map.