Just try this method , also Mac mini and new Mac has different preferences , in new version of Mac OS high Sierra its not sure it will work and using target disk mode it will take hours to transfer the data .
Transfer mail data from one machine to another .
Take back up of all mails in V 5 folder : Method to copy mails in V5 folder .
Click on Go on top menu bar , hold option key click on > library > select mail folder > right click on mail folder there itself > click on copy mail > right click on the desktop > click on paste item .
Entire mails are copied to V5 folder and V5 folder will get saved on the desktop .
Note : For Mac OS High Sierra the folder will be V 5 , For Mac OS Sierra the folder will be V4 , For El Capitan - the folder will be V3 , and for OSX Yosemite the folder will be V2 .
Take a USB stick and copy V5 folder into it , once it is copied right click on the USB stick and eject it .
Insert the USB stick in the second machine .
Configure new IMAP account in another machine , go to top menu bar , file > import mail boxes > import data from > select apple mail > click on continue > select the back drop folder then choose new .
When new IMAP account is opened , a new folder with all mails will appear in the mail side bar .You can rename the folder .
In your Mac mini the name of V5 folder will be according to the version .
