"قَلَم اَلْأُسْتاذة بُنِّيّ."

Translation: The professor's pen is brown.

[Zarpada]

How would you say "the professors brown pen"?

[TJ_Q8]

قلم الأستاذة البني (AL is added to the adjective بني)

In this case the adjective is said to be "attributive" and hence it follows the noun it describes in status (number, gender and definition by AL)

[StevenWest12]

Does this mean there is no way to mark possessive for 3rd person full nouns?
... Also, how would you say "a professor's pen"?

[TJ_Q8]

a professor's pen: قلمُ أستاذٍ
if you by 3rd person possessive like (his pen, her pen) then it is possible of course. That would be (قلمُهُ, قلمُها) respectively (respectively from right to left).

[Hassan323496]

Y'd say, قلم الأستاذ

[leo234017]

The professor her pen is brown ?

[TJ_Q8]

your sentence is not connected. It must have a form of Genitive (of-) relationship between words.

[Away54]

TJ_Q8,

I suppose leo234017 wants to say something like follows:

الأستاذةُ قلمُها بنيّ.

"The professor (fem.)" is "المبتدأ", "her pen" ("muDaaf muDaaf 2ilaih" الإضافة) is "بدل" of "The professor" and "brown" is "خبر". So, it is "The professor, ie. her pen, is brown". (I accept any input).