Microsoft will not offer upgrades for your exchange server. It will only  suggest you to upgrade your Exchange server to higher version.

Why you need to Migrate to 2016?

• Upgrade to Exchange 2016   maintains the  server infrastructure .
• Microsoft will not support for  bug fixes and security updates for Legacy Exchange server which may  cause data loss  of you business.
• Native migration methods are more complex and consumes more time.

You may search the best way for upgrading from Exchange 2013 to 2016  .

EdbMails for  Exchange 2013 to 2016 migration

EdbMails Exchange migration tool will help you  to perform  direct  migration  of mailboxes between any Exchange server.  Quickly subscribe to Exchange migration plan and  get it  done the migration of mailboxes from Exchange 2013 to Exchange 2016.

To know more Hosted Exchange Migration | On-Premises Migration | Office 365 migration from Exchange 2010