A 2010 FIDH monograph lists the group as one Islamic Jihad (''Mujahedeen Jamaat''), linked to the Muslim Brotherhood movement, which would identify it with the Islamic Jihad Movement in Palestine, usually referred to as the Palestinian Islamic Jihad (PIJ) in the West. The Russian Wikipedia offers Harakat al-Jihad al-Islami fi Filastin and Jamaat Mujahideen as alternative names, which seems to fit, and at least once source identified PIJ as the group banned along with Jund ash Sham in 2006.
I'm not entirely satisfied with this answer, however. Jihad, Jama'at, and Mujahideen are all extremely common words for naming (and nicknaming and aliasing) such groups, and other sources state that PIJ is not a Russia-designated terrorist organization. I would think the activities of the Islamic Jihad Union (IJU), a splinter group of the Islamic Movement of Uzbekistan (formerly the Islamic Jihad Group), would make it a candidate, but the IMU is already listed on its own, and I cannot say as to whether the new group is recognized as independent of it.