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B is right option . After resolving the conflict you need to update issue log first and then Leeson learnt. What you will update in Stakeholder Register ? The questions does not say any thing specific that it was because of any issue with stakeholder management /engagement .

Hi Anchal,
you don't need to update the risk register, as there is no risk.. the impact on the delay is here already and the conflict is closed
The lesson learn is the best solution as it will help you to avoid this issue in the future