ANSWER: We don’t have a specific hadeeth telling us. Therefore, if someone is paying alone, he should say it as he is rising from sujood. But if he is leading the congregation, he should say it as he is rising from jalsatul istiraha and Allah knows best. 

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ANSWER: If it sustained the injury without your intervention or fault, this can still be slaughtered for eid. https://islamqa.info/en/answers/39191/if-the-sacrificial-animal-becomes-damaged-after-selecting-it

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