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Foreign police and VPN

For example, user from Russia uses VPN-service which obeys US jurisdiction. This user did fraud on russian territory and russian police started haunting him. Everything they have is IP address of VPN-service. Will US VPN-provider (PrivateInternetAccess for example) share logs with russian police if they ask for it? Is VPN-provider able to refuse to share logs with non-US police? And yes, this user didn't stole billions from US banks, he just shared private photos for example.