Diddy 's working hard behind bars ... wrapping up after an honest day's work in new videos obtained by TMZ.

Check out the clips of the music mogul wrapping up his work for the evening on Friday at Fort Dix's media library located in the chapel, where he helps gives movies and religious materials to inmates. TMZ.com

Diddy, wearing a brown knit cap to cover his gray hair, seems to be readying to stay for awhile ... removing his scarf and blue coat to reveal his gray prison uniform. Later on, he puts the jacket back on and takes his leave.

We've also got video of Diddy without his cap on, fully highlighting his gray locks, while he stops to chat with other inmates in the hall. The convo seems good-natured before Diddy walks on down the hall. TMZ.com

We've shared numerous photos of

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