My understanding is that you are running mobility service version 9.62 for Azure Site Recovery and are wanting to update the kernel on your VM. Let me know if I am misunderstanding something.
The page here lists the mobility service version and the compatible kernels.
Since you are running 9.62 you will want to update your kernel to one of those listed here.
sudo apt-get update
sudo apt-get install linux-image-6.5.0-1023-azure
Is that the information you were needing? Please let me know if you have any questions or run into any issues.
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