Suppose we have a ticket with estimation of 4 units and this ticket was half done in one sprint and moved to next one.
Will it make difference, when we did re-estimation?
One option is to change estimation before sprint closed and then to move ticket and another option is to close sprint, move ticket and the re-estimate it.
What is correct way? Suppose 2 of 4 units were spent and we want to account it in a report.
Regard the following burndown report of 2-week spring
Apparently it goes down once ticket is completed. But suppose we have long ticket and the end of the sprint. Suppose it was not done this sprint and was moved to next one. How will it count.

Your estimation for that ticket did not change and you do not need to reestimate. You only are only moving the ticket to another sprint. If you want to include that 2 units of work in your reports, then it is a matter of your timesheet application, not the estimation or the sprint itself.