When migrate users from Lotus Notes to Exchange, mailbox size is increased 3 times (4288676)

This is because of the difference in compression used to store the data in Notes and the method used in Exchange.

Domino uses LZ1 compression, see here for more details: https://www-10.lotus.com/ldd/dominowiki.nsf/dx/use-lz1-compression-for-attachments

Then there are compression methods used for the body of the email which can also cause changes in size.

If DAOS (Domino Attachment and Object Service) is being used, there are other considerations. See here for more detail: https://www-10.lotus.com/ldd/dominowiki.nsf/dx/DAOS_Deployment_Guide

There is nothing to resolve here. Migrator for Notes to Exchange is working as designed.

There are some options you have going forward:

1) increase the storage capacity in Exchange