There at least 4 persons and several historical dates that could be named while answering this question.
In 1917, a Finnish inventor Eric Tigerstedt patented a "pocket-size folding telephone with a very thin carbon microphone".
In 1961, in the Soviet Union a Russian engineer and inventor Leonid Kupriyanovich presented a pocket automatic radio phone, which could fit in the palm of a hand.
In 1973, in the United States John F. Mitchell and Martin Cooper of Motorola showcased the first handheld cellular mobile phone, using a handset weighing 2 kilograms.
In 1983, the Motorola company introduced DynaTAC 8000x, the first commercially available handheld mobile phone.