How to sync icloud mail notifications between iphone and mac?

Question

iOS

There are:
iphone 4s (iOS 8) and MacBook pro mid 2014 (OS X 10.10 Yosemite)
1) When mail arrives, a notification appears on the poppy and on the iPhone (standard mail clients). If you view mail from a poppy. Then on the iPhone there is a sticker on the icon (red one) they say there is unread mail. Can this be fixed?
There is no such problem with gmail mail (when reading mail from a PC, the notification on the phone disappears instantly)
2) If mail arrives and the standard mail client (Mail) is not running on the poppy, then the notification does not appear, which is extremely inconvenient (there is no sticker on the icon). It can be fixed?

Answer 1

Perhaps PushBullet will help you