A vet told us to add some crushed pineapple to their food - they don't care for the taste coming out the other end! Worked for the one dog we tried it on
Pineapple often works due to the pectin and it acting like a digestive enzyme.
At 4 months of age if could be behavioral and will outgrow. On the other hand it could be a deficiency and the sooner you determine, the better of the pup will be.
If a deficiency, it is mineral deficiency, not a vitamin deficiency. It can also be a digestive enzyme defieciency, which feces is often high in and this could help the process.
I have helped several coprophagia cases and in most of them, the situation was addressed by addressing the entire digestive tract. A digestive enzyme should be added - either purchase one at your health food store, or add pineapple, apple cidar vinegar etc.. A good probiotic should also be added to help the process. You can purchase in your refrigerated section of your health food store and ensure there are at least 1 billion live cells in it.
You may want to also add apple cidar vinegar (1 tbl) to the food a couple of times per week and see if that helps.