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Hello and thanks for trusting me to help you and your pet today. I am a licensed veterinarian with over 30 years of experience and would be happy work with you.
It is possible that the cough and the heart murmur are not related, but it should definitely be evaluated. Cats can cough for various reasons, including cardiac and pulmonary disease, but since there is signs of possible cardiac disease, it warrants pursuing that as a possibility. When there is heart valve disease, the heart can become enlarged and as it progresses, can lead to fluid in the lungs, both of which can lead to a cough. There are medications that can help to control the fluid retention as well as to help the heart pump more effectively, so if heart disease is identified, there are things that can be offered to extend his quality of life time.
I hope this is helpful. Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please reply so I can clarify for you.
My posted replies are for general education only and not meant as a diagnosis. Only after a thorough veterinary examination can a diagnosis for your pet be made and specific treatments be advised or medications be prescribed.