If your iPhone email accounts are configured as IMAP then this is all very simple. Just get any old email program (but not Win10 email) on your laptop and configure the mailboxes as IMAP accounts.
There will then appear exactly the same as on the server, as seen on your iPhone and via Webmail.
Personally I favour Outlook 2016 as (also utilising an @outlook.com email address) that facilitates good email management and coordination of contacts, diary and notes between the PC and the iPhone if set up properly. I have an iPhone, two iPads and three laptops all being kept in sync with that approach.