How to use the Rules and Group modules to send a privatemsg to users of a role in a group?
Have a look at Comment #2 in issue # 2603136 (from the module maintainer). Here is how it looks like (I added the bold markup in it here):

Meaning you can already use Rules to:

Add a new Group
Create a new GroupMembership and save it (the equivalent of $group-&gt;addMember())
Add or remove a GroupRole from a GroupType
React on new GroupMembership or Group entities
…

What hasn't been done yet is custom Rules actions or conditions. Seeing as 90%+ of Group is pure Entity API CRUD-operations, there has been no custom Rules code yet given how much you can already accomplish out-of-the-box.
Useful Rules we may add could be:

E-mail all members of a Group, optionally filtered by GroupRole
Easier-to-understand labels for the above list: &quot;Member joined group&quot; sounds easier than &quot;GroupMembership entity is created&quot;
Feel free to add here


As per the bold phrase above, I think the exact answer to your question is &quot;Such Rules condition is not available ... yet&quot;.
Plan B
However, since you're also using the Privatemsg module, you may want to have a look at the community documentation about Privatemsg-Rules Integration, especially the child page about Introduction to Privatemsg-Rules: it lists the various Rules Events, Conditions and Actions you have available.
More important in the context of this question, is what's explained in the child page &quot;Message notification via email depending on user's role&quot;.
See where I'm going ...? No? Well: if you can think of a way to assign a role that corresponds to the name of the group (so 1 role for each role), you have an alternative solution that functionally will do exactly what you want to do. Obviously, 1 role for each &quot;group&quot; is only manageable if you don't have dozens (or hundreds?) of groups ...
Note: I haven't checked it yet, but it may well be possible to use the Rules module to auto-assign such role automatically when a user gets granted access to a group (Homework for you? Or ask a new question?).