Sign in with the same Apple ID & password say example1@icloud.com on your iPhone & Mac and connect both with an usb cable .
Click on finder > general > sync
Let the bar be completely loaded .
Open your mailbox in iPhone
Click on edit option on the up-right corner
Click on “new mailbox” option on your down-right corner ,
In the new mail box , in the name section enter your iCloud id say example1@icloud.com
And set your mailbox location as per you requirement (iCloud / gmail) - prefer iCloud
Then again click on edit , you will see your apple id , under it you will find an option of “new mailbox '’on your right corner > chose the name for your folder and add the mailbox location ( iCloud id )> click on save > finally click on done .
The folder is created in iPhone , open www.icoud.com in mail section in the bottom left corner click on refresh , the mail folders will be visible after few moments , then open IMAP account , under iCloud section in the bottom click on drop down arrows all mail folders will appear .
How to transfer mails from Mac to iPhone / iPad , even they are signed in with same Apple ID and password say example1@icloud.com
In iPhone go to settings > in password and accounts > click on add account you can select the desired account it could be gmail , enter gmail address and password and sign in it will prompt to check calendar , mail , notes , slide the box of it the apps data will start syncing .
there is an option fetch new data - push > in iPhone
You can connect the iPhone and Mac using usb cable and sync them https://support.apple.com/guide/mac-help/wi-fi-syncing-mchlada1d602/10.15/mac/10.15
https://support.apple.com/en-in/guide/mac-help/mchlde9a31f1/10.15/mac/10.15
The mails from Mac / iPhone will sync and take time ( the fast way is sync complete data ) they will be mirrored , you delete a mail from Mac it deletes in iPhone , make sure all the mails should be read ( no blue dots on each mail message ) https://support.apple.com/en-in/guide/mail/mail0025/mac