Hello ricardoespana,
Firstly, the arms themselves are quite probably genuine. That is to say they were probably granted to this Milner person by the College of Arms.
Secondly, whoever drew this was not from the College - there are mistakes in the drawing which the college would not make.
Thirdly, there is a popular misconception that there is a coat of arms for every person - not true. The widely called "Family Crest".
Fourthly, it is my belief that your grandfather fell into this trap and bought this image thinking it was related to his family - it probably is not.
This is taken from The General Armory.
Regards
Chas