It is considered courteous for a man to help a lady on with her coat. Make it an efficient, smooth and quick gesture.
Her coat should be held up by the shoulders, or between the collar and the shoulder seam.
It is important to position it so that her arms can slip in easily. The coat should be lifted onto her shoulders as she puts her arms into the sleeves. It should then be lifted slightly again to make sure it settles correctly on the clothes underneath. Never smooth down the lapels or tuck in her scarf.