Emails sent from iPhone don't appear in 'Sent' in Mac OS Mail despite both using same IMAP 'Sent' folder

Here's my issue (IMAP account on both devices):

• If I send an email on my MacBook, it will appear in both the Mac OS Mail 'Sent' folder and it will also appear in the 'Sent' folder in my iPhone's Mail app, which is great.
• But the other way around doesn't work - if I send the email on my iPhone, it does NOT appear in the 'Sent' folder on the MacBook.
• I've checked the advanced settings and both of them are set to store sent messages on the server - IMAP 'Sent' folder - spelled identically: one word, upper-case 'S' for 'Sent".
• I've looked for any filters, rules or blocked senders (not that I'd block myself) just in case, but can't see anything that would cause it.
• I'm not using a threaded / conversation view on my MacBook, so it's not that the message might be hidden within a thread as I have it set to show every email individually.

If anyone has any suggestions for other things to ry, please do say as it's quite annoying to only have the full history in one place but not the other.