Roles & Capabilities list and user permissions are fully independent between subsites. So problem with access is related to the main site only in the part of the replication roles from the main site. You should get exact copy of permissions you grant to a roles at the main site after replication.

Try to grant ‘edit_posts’ in addition. Just in case it will help.

If you turned ‘ON’ the “Activate “Create” capability for posts/pages/custom post types” option at URE’s Settings then you have to grant ‘create_prosforas’ to a role in order it can add new ‘prosfora’.

Another assumption,
do you have ‘Activate user access management to editing selected posts, pages, custom post types’ option turned ON at URE’s Settings? If Yes, there a conflict is possible, in case, if ‘posfora’ CPT is defined with own custom user capabilities and developer check some of those capabilities directly in the code, e.g. current_user_can(‘cst_edit_prosforas’).
In this case URE can not help with redefining CPT capabilities. It works correctly only in case code takes capability to check directly from CPT definition, like
$cpt->caps['edit_posts'] (just for example) not ‘cst_edit_prosforas’.