One of the famous 19th century Jewish-born missionaries was Joseph Wolff, born in Bavaria in 1795, who converted to Catholicism (1812). He studied in Rome, but was eventually expelled for heresy. An English banker based in Rome named Henry Drummond brought him to England. There he became a Protestant and was signed up as a missionary for the London Society for the Promotion of Christianity Amongst the Jews. When the Society did not send him on a mission, Drummond himself financed a trip to the Middle East for him, including to (what I will call) Israel. This he did in 1821-22.
First, a digression. The following was published in The London Magazine in 1827:
Wolff then published an account of his travels in the form of journal entries, and very interesting they are. Included in his account is a meeting with one of the foremost students of the Vilna Gaon, Rabbi Menachem Mendel of Shklov (1750-1827), who had emigrated in 1808 with a group, was then the leader of the Ashkenazim in Israel.
Here is a letter written by him:
Wolff's complete account deserves to be reprinted, so here it is:
I know that this is unusually long, but it's well worth reading. If you want to read the parts I left out, plus much more, do see the Missionary Journal and Memoir of the Rev. Joseph Wolf, Missionary to the Jews.
Here is an image of him preaching in the Holy Land: