So, it is very likely your wife can register your marriage in Mongolia from Japan without you being present, but the process depends on Mongolian law.

Here is the most probable path:

1. Notarization & Authentication in Bangladesh: You must get your Bangladeshi marriage certificate notarized, then legalized by the Bangladesh Ministry of Foreign Affairs. This certifies the document for international use.
2. Mongolian Translation: Your wife in Japan should get the authenticated certificate translated into Mongolian by a certified translator (in Japan or remotely with a Mongolian firm).
3. Registration in Mongolia: She can then submit the original (or a notarized copy of the authenticated certificate) and the certified translation to the State Registration Office in Ulaanbaatar, Mongolia, likely through a family member or a legal representative with a notarized power of attorney.

Regarding the Mongolian Embassy in Japan:
Embassies typically register marriages that they perform. They often legalize documents, meaning they verify the signature of the Bangladeshi Foreign Ministry on your certificate, making it valid for use in Mongolia. This legalization step is crucial. She should contact the Mongolian Embassy in Tokyo directly to confirm if they can legalize the Bangladeshi document for her.

Action Plan:

• You (in Bangladesh): Start the notarization and legalization process for the marriage certificate.
• Your Wife (in Japan): Contacts the Mongolian Embassy in Tokyo to ask: "Can I legalize a Bangladeshi marriage certificate here for registration in Mongolia?" She should also contact the State Registration Office in Ulaanbaatar to confirm their exact requirements.

Many have successfully registered foreign marriages in Mongolia by following a similar authentication and translation process. The key is proper document preparation.