Is there a way to restrict member/group from sending PM only, without changing their Primary Group?

I have tried setting suitable permissions in a Secondary Group, but Primary overrides this  

If not, is this something that could be introduced in Restrictions, please?

 

If you're trying to stop a spammer, troll, or otherwise a troublesome member from sending PMs, I doubt that restricting them from sending PMs but not receiving would actually stop anything. They'll just find another way to harass others, whether that would be through a chat, a post, or even a status update. In fact, it may encourage other members to harass that one member knowing that he or she cannot reply. It seems like a better option just to restrict messages all together, even if it is on the "extreme" side. If you have to give an admin message, you could always give them a 0 point warning.

If you must though, you could always edit the template directly. Find what the secondary group ID is, and use this in your template:

core->front->messaging->conversation
Replace:

<div data-role='replyArea' class='ipsAreaBackground ipsPad ipsSpacer_top'>
	{$conversation->commentForm()|raw}
</div>

With this:

{{if !(\IPS\Member::loggedIn()->inGroup( 3, $permissionArray=TRUE ))}}
	<div data-role='replyArea' class='ipsAreaBackground ipsPad ipsSpacer_top'>
		{$conversation->commentForm()|raw}
	</div>
{{endif}}

Replace the 3 with your secondary group ID.

Alternative: