If you’re the one taking the screenshots, then the answer is a resounding No. Facebook doesn’t inform the person if you take a screenshot of their profile picture. Unlike Snapchat, here the only notification you’ll get is from your phone that you have taken a screenshot.
The same can be said of the Facebook Messenger too. No matter whether it’s a chat with a friend or a complete stranger, the screenshot functionality will act more or less like in any other app — just the phone informing you about the screenshots.
But then, if you are one who is genuinely concerned about your pictures floating about in the social media, there’s not really much you can do. Except, of course, never publishing a picture or limiting the audience to your friends.
Facebook has a robust built-in Share alternative which you can use if you aren’t comfortable taking screenshots. All you have to do is tap on the share button and send it over to your friend who is already on Facebook.
If that’s not the case, you can tap on the three-dot menu and select the Share external option, which uses a lot of third-party options like Whatsapp, Messages, Instagram, etc.
This profile picture guard shows up watermark-like lines upon download and restricts the screenshot operation till the time you are in the profile picture.
Similarly, the option to share or save won’t be there for the protected profile pictures. And speaking of the desktop version, you’ll no longer be able to save the picture as an image file. Instead, it’ll be downloaded as an HTML file, which is the case with most of the websites.
But as is the case with most of the experimental features, it’ll be quite some time before it’s bug-free.
The bottom line is this, Facebook doesn’t send notifications when you take screenshots, but still, an ethical way would be to use the share features. And if you’d like to take it a bit higher, take the consent of the person before hitting the download button. But then, as they say, once you share something on Facebook, it’s equal to shouting out the same to the whole world.