He used several pseudonyms during his intelligence operations: e.g. Rudolf Schmidt, Nikolai Vasilevitsh Grachev (Николай Васильевич Грачёв) and Oberleutnant Paul Siebert.

According to a report submitted by Josef Witiska to Heinrich Müller (and cited by D. Medvedev in his memoir about Kuznetsov), "Paul Siebert" and his accomplices were detained and shot by the Ukrainian Insurgent Army, which then informed SS-Obergruppenführer Hans-Adolf Prützmann about the incident.

According to official Soviet version, Kuznetsov was killed in a firefight with members of the Ukrainian Insurgent Army near the city of Brody on 9 March 1944.

In another version by the Ukrainian Insurgent Army, Kuznetsov and his associates were detained in the village of Boratyn near Brody, dressed as German soldiers.

[5] A 2007 attempt was stopped by the Russian Foreign Ministry, which claimed that "such a move would open a kind of Pandora’s box and give Ukrainian nationalists a reason to launch a campaign to transfer other graves of Soviet soldiers buried in Ukraine.

"[5] A 2018 attempt was prevented by the Lviv authorities, who claimed that such a reburial could not be considered while Ukrainian prisoners were being held captive in Russia during an ongoing Russian military intervention in Ukraine.

[5] Colonel Dmitry Medvedev, who oversaw Kuznetsov's activities, repeatedly attributes him discovery of a planned Nazi operation against the Tehran Conference of Allied leaders.