There is an asterisk that you have to be at the right glide velocity, but yes: they'll have the same glide angle. The leaden one will just go significantly faster. And yes, it does sound unlikely. That's why I made my previous comment.
Here are a couple of many posts on the topic:
- https://gronskiy.com/posts/glide-ratio-lift-to-drag-and-weig...
Thanks for the links. Weight may cancel out of the equations, but (being a bit pedantic) I suspect 'glide angle in independent of weight' only holds up to a point. Taking things to extremes, if the glider is heavy enough that you are going to have to go supersonic then I suspect a lot of the assumptions become invalid.
NB/ spherical cows are unable to glide in a vacuum.