Can I make a power of attorney for my sister to write a statement on...?

If you mean an application for dissolution of marriage to the RATS authorities, then only spouses have the right to submit an application. If the husband and wife have agreed between themselves, then the spouse who is in Ukraine and has the opportunity to visit the RATS body, submits two applications for divorce at his place of residence: on his own behalf and on behalf of the other spouse.

In the event that it is impossible to come to an agreement with the other spouse, and you yourself do not have the opportunity to do so, you can make a power of attorney for your sister to file a lawsuit for divorce with the court and take all actions regarding the divorce on your behalf.