When the player that DOESN'T have the mount gets a new equipment item, there isn't the option to equip it. When the tooltip is clicked on, the only button is "Done" The player WITH the mount does have the "Equip" and "Done" button options
All settings are the same on both characters, and I tested this with both dropped equipment and equipment that is rewarded from a quest
I had the other player leave the mount before turning in a quest and the "Done" button was back then
