Plasmodium causes malaria which goes through mosquito female anapheles through some of its life stages. But I am not sure which scientist experimentally demonstrated the life cycle of plasmodium. In texts, I found following text which talks about the work of Grassi in 1898:
And following data supports the fact that Laveran also worked on the life cycle of plasmodium in 1880 which is even way before than Grassi's 1898 experiment.
By chance, but also thanks to his tenacity and patience, he had seen the exflagellation of a male gametocyte, a phase in the life cycle of malaria parasites which usually occurs in the stomach of the Anopheles mosquito. https://www.cdc.gov/malaria/about/history/laveran.html