The phrase "a former inmate of" is correct and usable in written English.
You can use it when referring to someone who has previously been incarcerated.
Example: "He is a former inmate of the state prison, where he served five years for theft."
Alternatives: "an ex-inmate of" or "a previous inmate of".
Marlon Hamer is a former inmate of HMP Manchester.
Al-Ajmi was a former inmate of the detention camp at Guantánamo Bay.
This is the Justice and Development party, a studiously moderate lot, led by Muhammad Suwan, a former inmate of Qaddafi's jails.
"When the British came to our country, they said everything we are doing was barbaric, was wrong, inferior in whatever way," Mr. Zuma, a former inmate of the Robben Island prison, said to a South African newspaper.
"To be honest, I was ecstatic," said Jason Porter, a former inmate of Suffolk County jails who said he had been in out and of jails for about 14 years and was among those who filed a lawsuit.
At Hyde Park Corner a counter-service, held by a Lutheran minister (a former inmate of a Russian prison camp) by the Artillery war memorial, had drawn only some thirty people, and his words never reached the marchers at all.
The groups want to provide a counselor and a "coach," a former inmate, for each new person cleared of charges.
He was joined by investigative journalist Eric Schlosser Chris Munroo the managing editor of Tracker magazine which was Australia's most read Aboriginal Affairs publication until it was shut down last year and Debbie Kilroy, a former inmate and founder of Sisters Inside, a group that advocates for the human rights of women in the criminal injustice system.
Eventually we meet Janusz (Andrei Kashkar), who survived the Lodz ghetto, and Rosa (Helena Yaralova), a young former inmate of a Siberian prison camp to whom he extends fatherly comfort.
The initiative was welcomed by a veteran of the anti-apartheid struggle, Ahmed Kathrada, a former inmate and close friend of the late Mandela.
The entire document is available here, or alternatively, an excellent memoir of a former inmate who escaped the unimaginable horrors of the camps gives a first-person account.
