Motorola was the first company to produce a handheld mobile phone. On 3 April 1973 when Martin Cooper, a Motorola researcher and executive, made the first mobile telephone call from handheld subscriber equipment, placing a call to Dr. Joel S. Engel of Bell Labs.otorola was the first company to produce a handheld mobile phone. On 3 April 1973 when Martin Cooper, a Motorola researcher and executive, made the first mobile telephone call from handheld subscriber equipment, placing a call to Dr. Joel S. Engel of Bell Labs.