I rock my baby to sleep or my wife nurses him till he sleeps. However the moment we put him into the cot, he wakes up and starts screaming. Then we rock him to sleep and when we put him into the cot, he continues screaming. The cycle repeats till we are very shag. Anyone has ideas how to solve this?

Think of it from a baby's perspective. He's huddled and cuddled in his mummy's womb for 9-10 months. All his demands were met, perfect temperature with endless supply of food and constant rocking from mummy's actions. He's suddenly in this big world - no constant cuddles etc. Look into co-sleeping on the same bed. Google on safe co-sleeping. Your wife knows how to latch the baby? Good. Get her to learn how to side latch her baby so that she can rest and baby can suckle for comfort for as long as he wants. Suckling helps soothe the baby so much that it brings comfort to them.