My girlfriend has dry lip cracking for almost 3months sinve she works in air conditioned close office. Any medication recommended for her? Thanks

Hydration. Air conditioning drys out the air a lot. As a result, staying hydrated is one of the best things she can do to help with not only her lips but with dry skin in general. Non-petroleum-based lip balms can also help but are no substitute for drinking lots of water.
Chap Stick. It is recommended that she use lip balm to protect lips from chapping and cracking. They have medicated versions that are couple with analgesics to reduce the pain from dry cracked lips. If it becomes worse, looks infected, or doesn't improve with use of the lip balm she should see a physician to determine to root cause.