Although the length of my translation is larger, nevertheless I think there can be found a way to place it properly. The translation itself is the most precise option among the suggestions.

It translates into Russian basically word for word, no additional explanation of the function is needed, except I decided to add that media files cannot be saved on the device.

Using words "пользователи" instead of "участники" will be better on reading (because we talk not just about members of group, but about any user).
Using word "файлы" instead of "медиафайлы" helps to reduce the amount of symbols, while it's still clear to understand for Russian users.

I have switched places parts about forwarding messages and saving media files as it allows for better understanding that both of these actions cannot be done by members of this group inside this particular group. In all previous suggestions, the order is the same as in the English version and in Russian, it gives a feeling that members of the group won't be able to forward messages from the group and won't be able to save any files at all (even those not in this group).

It depends upon the context but might also be better as a future form.