Ubiquitin, Sephardim have lived in Amsterdam, the US, France, and other European countries and cities since their ancestors fled the Inquisition from Spain, Portugal, etc, which are countries in EUROPE. There are numerous old Sephardic shuls in all over Europe. The beginning of the Sephardim is similar to Ashkenazim who immigrated to Europe from Greece and the Levant.
Not as many Ashkenazim have emigrated to the Middle East over the centuries but there were pockets of communities and individual Ashkenazim who immigrated to the ME, most notably the Ashkenazim living in Israel over the past few centuries.