Here is the solution: use dd instead of cp, and do it in such a way:
dd if=/dev/{sourceLVMGroupName}/vm-{$VMID_SOURCE}-disk-{#} of=/dev/{destLVMGroupName}/vm-{$VMID_NEW}-disk-{#}For example, if I have such a setup:
# pvscan
PV /dev/sdb VG VG_vmstore lvm2 [931.51 GB / 899.51 GB free]I simply do
dd if=/dev/VG_vmstore/vm-101-disk-1 of=/dev/VG_vmstore/vm-102-disk-1