I miss having a notification that I received a message in my mailbox.
Currently, if you send a message to another player, they will only know they have a message in their mailbox if you ask them to look; similarly, you will only know you received a message if the other player notifies you.

With the game's own notification, we would receive a notification on the game screen.

For example: Sometimes I need to talk to a player, but I never see them online, so I would leave a message for them in the mailbox and they would see it as soon as they logged into the game.

It would also help with chat trading. Sometimes I saw a player selling something in chat trading, but when I messaged them they were no longer online. With the game's own notification, they would see my message in the mailbox saying that I am interested in the item or Pokémon they were advertising, and they would contact me to negotiate.

This improvement to the mailbox would greatly facilitate communication between players, especially because of the different time zones.

+1 

I would love a little notification saying "1 unread mail" and having more informations. It will help for future giveaways via the redeem code or guild giveaway.

Bump, need a mail system update with a little notification.

+1