BuddyPress doesn’t notify anyone when their activity gets favorited, the core notification system covers friend requests, mentions, and group activity, but not favorites. BuddyPress Favourite Notification closes that specific gap.
What It Does

Two things, and only two things: it lets members mark or unmark an activity as a favorite (already possible in core BuddyPress), and it sends a live notification to the activity’s owner when that happens. Nothing else, no leaderboards, no featured-activity dashboards, no extra settings screen.

Setup is install-and-activate, no configuration screen. It does need the BuddyPress notifications component enabled to work.
Worth Knowing
The plugin hasn’t seen an update since late 2024, not abandoned (it’s a two-function plugin with little surface area to break), but old enough that it’s worth a quick staging test before deploying on a site running a recent BuddyPress release.
Pricing
Free. Download it here.