The 24-year-old has been an ever present for the London side during a loan spell.
Tanganga was outstanding in a 1-0 win over Birmingham City at home, scoring the winner.
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"Japh's got great pedigree, he's got a great CV in terms of games at the top level and playing in Europe," manager Neil Harris said after Saturday's win.
"Sometimes you have to be a different player here, and the reason I'm at the football club is to try and teach the players what a Millwall player looks like, whether that's a goalkeeper or a center-half or a center-forward.
"All I said to Japh was just to make your decisions and I'll support you, but you can be as aggressive as you like.
Ultimately, he's headed the ball a lot (in both boxes) and to be a good Millwall center-half you have to do that."