Top glass broken, display still working.

You can, but you need to purchase the entire LCD and digitizer assembly. The LCD and digitizer are fused together. Trying to separate the glass from the LCD is time-consuming and you risk damaging the LCD in the process, resulting in having to purchase the whole assembly anyway. And you need the tools to disassemble the phone.

Depending on your model phone and where you get the assembly, it can run in the neighborhood of $180.

If you can find a reputable repair center, it will save you the time and headache, even though you will have labor charges on top of the $180.

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Thanks.

Caveat emptor! The repair kit is inexpensive, and the procedure for removing the old glass looks deceptively easy. Don't be fooled. None of the instructions I found mentioned that when you warm the adhesive to get the glass off, there is a good chance the LED will come up instead. Then, you need the entire front display at much greater cost and a 36 step tear down of your phone. Only do this if you are desperate or daring, and NOT your wife's phone.