Before or after the suicide attempt by LHO? The Russians like the Americans soon realized he was nothing but a clown.
I edited it a bit, so maybe you should read it again.
But to answer your question,
after he "tried" to kill himself.
Obviously.
Here it is again for you:
Are you sure that Oswald really tried to kill himself? Did he write in his "Historic Diary" that he cut one wrist, or both? What did the records at Boskin hospital say? If "the Russians wanted Oswald out of Russia," why, AFTER OSWALD'S SUICIDE "ATTEMPT," did the mother-in-law of a future false-defector (KGB Colonel Igor Kochnov, secretly to the FBI in 1965 and "overtly" to the CIA in 1966 as KITTYHAWK; look him up), Yekaterina Furtseva (the most powerful woman in Russia; look her up), override (future false defector) Yuri Nosenko (look him up) and demand that Oswald not only be allowed to stay in the USSR, but NOT be recruited by the KGB?*
*As related to the CIA and the FBI by false defector Yuri Nosenko and other Kremlin-loyal KGB agents