You're objectively wrong, and the information she shared from that group was the very definition of fake. Here's the exact comment that was shared from that group:

"R.I.P. Justin Allen 23, Brett Linley 29, Matthew Weikert 29, Justus Bartett 27, Dave Santos 21, Jesse Reed 26, Matthew Johnson 21, Zachary Fisher 24, Brandon King 23, Christopher Goeke 23, and Sheldon Tate 27.... All are Marines who gave their lives this week for you. There's no media for them... not even a mention of their names. We’re too busy talking about trying to get “Baby It’s Cold Outside” off of the radio. Please honor them by copying and pasting this post."

Except obviously, they didn't die last week as of that post. They died seven years ago. Now why would a large group share literally fake information like that? And why would you immediately jump in and attempt to discredit my argument given that I even gave you the name of the group? Take a cursory glance at them and their actions.

I may be missing something fundamental here, but I'm not sure what that post has to do with Russia or propaganda. You say it's obvious they didn't die last week, but it wasn't obvious to me upon reading - perhaps because I'm not American. But if there's no date in the text, maybe your mum just didn't remember the original event, thought some soldiers had died, and she would be honouring them with some copypasta?

I guess I don't see a need for a conspiracy, Russian or otherwise, to get people re-sharing posts on Facebook that explicitly say "if you don't reshare this you're a bad person".