There are 2 cities named Mogilev, one on the river Dnieper, the other on the river Dniester. The correct name is either Mogilev or Mogilev-na-Dniepre (literally Mogilev on Dnieper). The other was called Mogilev or Mogilev-na-Dniestre (Mogilev on Dniester), in 1920's it was officially renamed to Mogilev-Podolsky (Mogilev in Podolia).
The former and the one you are interested in was the capital of the eponymous governorate and is part of Belarus now. The difference in spelling is due to transliteration from different languages.
There is quite a bit of information online about history of the city. You can also check Wikipedia articles in different languages, besides English, such as Russian, Belarus, Ukrainian, etc, while using Chrome or similar browser to translate the page.
Did you check Yad Vashem site, there are multiple people with this last name that come up in the search: https://yvng.yadvashem.org/index.html?s_lastName=briker&s_place=mogilev.