"Facebook claims its motive for threatening Ad Observer is that browser plugins and extensions, like Ad Observer, could violate Facebook users' privacy."

Yes, but so can Facebook itself. And it has, many times. Facebook lacks credibility here. It is possible this research may even uncover further violations of users' privacy as it may reveal levels of targeting not believed possible based on the types of user data Facebook admits to having.

Can Facebook effectively block users from saving and sharing the ads that are forced upon them by Facebook and its advertisers?

Facebook would have to control what users choose to save from their browsers' caches and what they choose to do with that material, e.g., sharing it with researchers.

The legality of "scraping", fair use for research purposes and the general unenforceability of website TOS all stack in NYU's favour.

Laura Edelson, a researcher at NYU's Tandon School of Engineering who helps oversee the Ad Observatory project, said, "The only thing that would prompt us to stop doing this would be if Facebook would do it themselves, which we have called on them to do."

https://www.wsj.com/amp/articles/facebook-seeks-shutdown-of-...