Google is rolling out to some businesses the ability to respond to Google My Business messaging through your desktop browser. Previously you were only able to manage it from your mobile phone and before that, through SMS.
This was not yet announced but I see it on my own Google My Business account, and so does Henry H who posted about it on Twitter. Here is my screen shot, you can click on it to enlarge:
If you log in to Google My Business, click on your business and then you may see a "messages" menu item on the left navigation bar, that is where you can manage this. There is a new help document with how to use this and how to manage the messages.
I am happy this is now available for businesses to manage on a desktop browser. It can make it easier for customer support representatives to manage numerous messages at the same time in one single larger interface.
Forum discussion at Twitter.