Worminyourear wrote:
Emails visible in mail on my iPhone, OS 13.3.1 are not always visible on my Macbook Pro, OS 10.15.3 (although some are).
Is there a way to ensure both devices display all my incoming the emails?
You do not say who provides your email... non-the-less
Verify you are using the default IMAP protocol on both devices—this ensure the mail stays on the server and both device access the account. ( POP acts quite differently.)
synch should not be an issue in the Mail.app
The best trouble shooting advice to resolve an issue here is to delete the account on the MBP. in your Mail.app Then it is a simple matter of adding the account back in, typically this is all it takes to resync.
remember that all IMAP mail remains on the server and will still be there when you fire it backup.
If you have any custom "On My Mac" mail folders they remain untouched, those are client side and remain on your computer.
Add or remove email accounts in Mail on Mac - Apple Support