Vapor is different from cigarette smoke. But both are a foreign substance to the body, and it will react appropriately. Most people who smoke coughed when they first started smoking. Most vapors who start vaping cough. It's normal. It took their bodies some time to adapt to cigarette smoke, it will take some time to adapt to vapor.
It's as simple as that.
New vapors should drink PLENTY of water to keep their mouth and throat moist. The Pg and Vg present in vapor attract water and can dry out mucous membranes. Sucking on some hard candy to stimulate salivary action can be helpful, too.
Advise new vapors that nicotine is absorbed differently than in tobacco smoke. Our bodies absorb the nicotine in vapor through the mucous membranes of our mouth, nose, and throat. So, it's not necessary to inhale vapor into the lungs to get the nicotine, just contain it temporarily in the mouth.
This might mean a different drawing technique from smoking. Tell them to imagine sucking on a straw in a thick milkshake. A slow, deliberate and patient draw into the mouth for 3 - 6 seconds. Hold for a second or two to absorb the nicotine. Then inhale in the lungs, or exhale through the mouth an nose.