Hello,
To treat undereye wrinkles, take rest adequately and eat healthy nutritious food containing lots of green vegetables. Try to avoid caffeine, because it promotes water retention and leads to the dryness of the eye. He should also apply almond oil or skin creams containing vit C or K,alpha hydroxyl acids and kinetin. If the symptoms are severe then it will be best to consult a dermatologist. Laser treatment, botox and other filler injections and chemical peeling may be done.
I hope it helps. Take care and please do keep me posted on how you are doing or in case you have any additional doubts. Kind regards.