Three Russian generals of that name are known but it is not clear if they had collections of art.

Akhlyostyshev, Mikhail Afanasyevich (1710–1784)
A Major General, he participated in the 1737 campaign and capture of Ochakov.

Akhlyostyshev, Mikhail Fyodorovich (1782–1829)
A Lieutenant General, hero of Napoleonic wars, actively participated in the War of 1812 (Napoleon's Russian Campaign)

Akhlyostyshev, Dmitry Dmitriyevich (1796–1875)
A Lieutenant General, he participated in the War of 1812, in the Caucasian War and in 1831 Polish campaign, was the Acting Governor of Georgia in 1838-1840, the Military Governor of Odessa in 1840–1848. In 1848, he became a senator.