He’s a very obvious Talmid Chochom, based on his translations alone, so I can’t imagine calling him Mister. Rabbi Finkel worked on a Tanna D’vei Eliyahu published by the Yeshiva as recently as 2013, so maybe he does in fact have email. Regardless, it isn’t published anywhere.
I’m wondering, why is it necessary for you to use email, instead of investing in a short telephone call? You can call Rabbi Finkel and ask if/how you can contact him via email, since that is easier for you. The call would only last less than a minute or two! Worst case scenario, he will tell you that he can’t be contacted via the web!
Independent rebbeim/staff at Yeshiva Beth Moshe have personal/private email formatted like this: “… @ybm.edu“.
I can not find any public resource that lists a contact email address for the yeshiva office, or administrator. If you are determined to avoid freely published telephone contact numbers, there is some information that can be helpful if you use google. There’s a Scranton Jewish community site to promote information and interest in the kehilla: Jewishscranton dot org.
Under the “community” link there is an education link. That page has a description of the 4 schools there. The Bnos Yisroel high school has a contact email address listed. The address is using Yeshiva Beth Moshe’s email domain. So apparently, Bnos Yisroel has or had some technical connection to the Yeshiva. I imagine they would have any online public contact information for the yeshiva – if it exists.
Perhaps you can send a quick email to Bnos Yisroel, asking for the email address that Yeshiva uses. Or request that they forward your email to the Yeshiva for you. Many yeshivos and Bais Yaakov type schools in consolidated Jewish Communities do not have a need to maintain a presence on the web. A listed address and telephone number serve their needs.
I still think it’s simpler to call Rabbi Finkel.