Google's John Mueller said he doesn't see an SEO problem with taking reviews left about your company on Google Maps, Yelp and other third party web sites and copying some of them or all of them to your own web site to showcase them. He said the one thing you should not do is markup them with review markup since they were not originated from your site.
John said this on Twitter:
From a Google SEO point of view, I don't see a problem with that. I imagine the original is more likely to rank for that text, but if you use that to provide context, that's fine (it shouldn't be marked up with structured data though). Maybe an iframe/embed would work too?
— John ☆.o(≧▽≦)o.☆ (@JohnMu) September 5, 2018
Google has guidelines against taking reviews from third party web sites and putting them on your own site with structured markup on them. Google said only the site that first received those reviews should use the structured markup.
But in terms of copying the review text and sourcing them, that should be fine said Google.
I do see this a lot for restaurants, app web sites and more.
Forum discussion at Twitter.