No you cannot spread angular cheilitis to another person because angular cheilitis is not contagious like cold sores and other mouth sores are.
So it's safe to kiss someone with angular cheilitis or be near the person who has angular cheilitis without worry about getting it yourself.
There's no possible way for the angular cheilitis to spread from one person to another.
The condition angular cheilitis can be caused by either a fungal infection or bacterial infection but it's not contagious.
It can spread from one side of your mouth to another side of your mouth but it cannot be spread to someone else.
You can help to treat angular cheilitis at home by putting some petroleum jelly or coconut oil on the corners of the mouth, which can form a barrier from saliva and help get rid of the angular cheilitis.