In this situation i would transfer colonies that grew on ampicillin plates to chlora plates, then choose the colony that cannot grow on chlora pates to make sure that i don't get the mutant.

Ok, if you grow transformed one's in chloramphenicol then you are basically selecting the false positive ones. There will always be few false positive ones that harbour the ccdB mutation, and there'll be colonies if you select them. Idea is to select based on ampicillin, and then check if it's a true positive by growing that in chloramphenicol.

My suggestion would be,

first, grow the transformed bacteria on ampicillin plate,

then select few single colonies,

now for each single colony, gently scrub/touch the colony with a sterile inoculation loop/pipette tips, then touch that loop onto a fresh ampicillin plate (mark the position where you touch),

finally, put the loop/tip into a falcon tube containing 5/10ml liquid media with chloramphenicol.

now, the colonies you selected primarily will grow in fresh ampicillin plate, so you can use them later once you are confirmed about their identity.

if any colony grows in liquid media, then that's false positive, discard that, use others.