Simple idea for the app (easy link to group)
When viewing a group post in the app, why not have the heading -- which is the name of the group anyway -- as a hyperlink to the group's page? That way you can easily find the group page to create a new post.
The 'back' arrow might take you back somewhere else, and you cannot currently get to the group except by finding it in the groups list under your profile. A direct link would be much quicker, and should be a simple matter to program.