I would say yes. If I was the student, I would ask the original teacher for permission to use her choreography and give her credit in program if there is one.

If there is no value to the choreography (to be stolen) then why does the student NEED to use it?

If it were me - I would ask permission.

I'd say write your own or get permission, If you don't think she'd give it you have probably answered your own question... If you find them difficult to write yourself, do you know someone who could help? or even adapt something from a DVD? also if she is still performing it and it's a small dance community where you are, people will have seen it maybe? better to do something new... I really struggled to write my first group choregraphy, but the sense of acheivement was worth it. :-)

IMHO it is not OK to perform a choreography without permission. ***UNLESS*** the teacher has given blanket permission for students to use anything she teaches. Many teachers do, and so do I. If I teach it to you, then it's yours to do with as you please. If I don't want someone to use it, I won't teach it.

But back to this specific case.

Is this choreo Teachers own original work? Then don't use it without permission
Is it a "public" choreo from a video or workshop? Then it isn't really "hers", it's public domain and no permission is necessary (though credit is nice).
A personalized adaption of a "public" choreo? Then it is "hers", and if I really loved the music/routine, I'd make my OWN adaption.
Did Dancer X do this number with Troupe as a Troupe number? If it was a troupe number, I wouldn't do it as a solo. I'd make my own solo to the music, if I loved the music that much.
Did Teacher teach the routine to Dancer X for Dancer X to use as a solo? That's trickier. If Teacher created this dance with/for Dancer X, I'd say Dancer X may have some rights to the choreography (work for hire, Teacher was paid to create a dance for Dancer X).
Otherwise, if the solo is Teacher's own work, get permission. If it's a "public domain" choreo, no permission is needed.

Other points:
Teacher regularly performs this choreo, so it's identified with her Troupe. For me, that's reason enough to not use it.

Dancer X left Teacher's Troupe months ago "not on best of terms". Another good reason to not use it

Is it LEGAL, most likely yes. Is it ETHICAL? Not in my opinion, unless the teacher expressly stated during the course of the class that this was up for grabs. Ethics are very different from morals or legalese. Typically, if I have to stop and ask myself if an act is ethical, the answer is "no"...

Student paid for the steps. Teacher taught what she was paid to teach.
Like a history class or Math class, its all going to be used later - We just dont know how.

If the ex-student did it solo - maybe it would be okay.
If the ex taught it to another group - SO Not Okay!

If it was me - I would create something new......

If your the exTeacher and its a year later, take it as Kudos - the ex cant figure out how to do anything new!

Ethical - No
But we know going into teaching these things that this is the Number One possible situation that will come sooner or later.

My question would be - why would the dancer *want* to perform that choreo in the first place? If she left the teacher, on bad terms no less, then just wipe the slate clean & start over...do a new choreo. If it's the music she likes, then use that music but create her own choreo. If it's some of the combos she liked, then blend them into a new number with her own spin on it to different music. If it's just because she needs a number she's comfortable with & it's the only one she knows -- well, honestly, that's not a big enough reason to open that potential quagmire.

From the sounds of it, this was a troupe choreography & it should stay with that troupe. Regardless of whether or not she is with that teacher, she is not with that troupe anymore either and that's not cool to do to the other dancers still in that troupe either. I almost find who choreographed it irrelevant because of the troupe aspect.

It's not ok for this former troupe member in any way, shape or form to use a choreographed piece learned w/in a troupe without permission and present it to the public.

This happened to a friend of mind who had her own troupe. She developed original choreographies for a troupe and former troupe members would perform it without her permission. She would occasionally retire choreographies and bring them back for special occasions or after two years or so. Since former members would pass the choreography to their students, the choreographies (one in particular) were seen over and over again in the dance community. People got tired of watching the same thing over and over. Dancers probably wouldn't want to watch this performance because they've seen X troupe perfom it - been there done that kinda thing. It also puts the choreographer in a pickle because she can't showcase her original work!

The other problem you run into is having great choreography just taken and duplicated and that choreo becomes muddied. Someone performs the choreography but not to the level to which it was intended. It doesn't do justice to all the work it took to put the piece together. If you haven't choreographed a piece before, you don't realise the amount of time, hours, tears (a least for me)and practice, practice, practice it takes to make something look effortless.