If your partner has bought tickets in Russia, they can sue Turkish Airlines in Russia. Russian consumer protection laws are very strong, so you will probably be able to claim all your expenses. Plus 50% fine on the airline if they will not compensate the expenses voluntarily. The process may be long (several months) and tiresome, but there is a good body of court cases specifically against Russian representative of Turkish Airlines, see, e.g., the all-Russian database of court cases.
The process would be as follows:
- Determine the exact information about the airlines representative (official address, ИНН, ОГРН, whatever).
- Send an official pre-court-case claim ("Досудебная претензия") by Russian post to their official address, preferably with post acknowledge of receipt ("уведомление о вручении"), this is a small card that will be mailed back to you as a confiration that the airline has received the letter.
- Now they have 10 days to pay you.
- If they don't, file a court case. As a consumer, your partner has the right to choose the court. This most probably will be raion court (районный суд) serving your partner official address (по месту регистрации); however, there are other options too.
- Wait for the court process, this will be very slow (several hearings with 1-2 months in between).
- If the court decides in your favor, collect the decision and "исполнительный лист" and file them directly to the bank where Turkish airlines have a bank account (you can guess, or check which bank processed your transaction, or make an official request to Russian tax authority).
For all the documents needed (pre-court-case claim, court case, etc.) you can find multitude of examples on the internet.
Also, I think you can contact any of law firms in Russia. Court cases according to customer protection laws are very common in Russia, and I guess there are many law firms that will take your case for a relatively small fee. You case is a bit unusual because the airline is not a Russian legal entity, but apparently they have Russian legal representative (see court cases above), so I guess law firms should know how to handle this.
See also:
https://www.kommersant.ru/doc/6664375 -- a newspaper article about similar cases.
https://forum.awd.ru/viewtopic.php?f=893&t=390100&start=2220 -- the biggest Russian forum about tourism, discussing how to sue Turkish airlines.