Hi, welcome.
No, it is not possible to replace Ubuntu with Zorin and keep everything from data (/) .
You can backup data and specific folder only.
If you have Ubuntu on 2 separate partition, root on one and home on second, than you can use those "home" partition on Zorin
Then, off to the Rescuezilla and read and study.
It is a stand alone software and you need to create a bootable USB to use it. Whole procedure is in GUI and beginner friendly.
In fact, I made a Rescuezilla USBs and gave them as a Christmas gift for my husband in addition to his daughter. The super penguin is absolutely cute!
A post was split to a new topic: Trapped inside logical partition
54 posts were merged into an existing topic: Trapped inside logical partition
Alright, thanks.
I do not want to risk my data. I'll just follow backup and restore.
If you think the problem is solved, you can mark the thread as solved by ticking 
This will help future visitors to this forum to find a solution they are looking for.