I managed to save the checked boxes using php (implode) and Mysql in a table. The values are divided with comma. You can see something similar here: PHP Multiple Checkbox Array. So, I have a table like this:
Id Values
1 1,3
It was the best solution at that time. Now I want to let user to change his options. I need to show him back the checkbox group, with boxes 1 and 3 checked. Thank you!