How do I sync my email accounts on Microsoft outlook laptop to iPhone?

Assuming the accounts are Exchange, or IMAP such as Outlook.com, Hotmail.com or pseudo IMAP such as Gmail.com, if you set up the accounts on both devices with Mail checked/ticked, then both devices will sync with the web server. There is usually no need to sync mail (or contacts or calendar) between devices.

You only have a problem with old fashioned POP3 accounts.

Yes hopefully they’ll tell you how to convert the account to IMAP online in Safari.

Or try Googling “How to convert xxxxxx.com email from pop3 to IMAP”