Abdul-Rehman Gul sent IS videos of shotgun executions in slow motion via a mobile phone in 2017.
While in a young offender institution he also shared an IS manual entitled How to Survive in the West.
At the time, the 22-year-old was serving life with a minimum term of four and a half years for three counts of wounding with intent.
Appearing at the Old Bailey on Tuesday 19th March via video link from HMP Woodhill, Gul admitted five charges of disseminating terrorist publications.
Prosecutor Alistair Richardson said the defendant was currently eligible for parole and was due a hearing soon.
Judge Richard Marks QC adjourned sentencing until April 26.