My partner suffers from extremely dry and cracked hands, lips and corners of the mouth. He moisturizes and uses cream several times a day but the prob

Dry skin and cracked lips are often a sign of nutritional deficiencies.  Without looking at a food diary or seeing how he eats I would say, your partner will most likely be lacking in B vitamins and / or essential fats.  Addressing this through nutrition would be my first plan. I would increase vegetables and fruit, ensure his carbohydrates are from whole grains, include adequate protein and oily fish in at least two meals weekly.

I would also include a good quality supplement to ensure he is getting adequate zinc, vitamin A and selenium which are also important for skin health.  Sufficient fluids are also key as dehydration can also dry out your skin. Aim for 2 litres  of water daily as a rough guide.