A volume group consists of whole physical volumes. A physical volume consists of many extents (an extent is typically 4MB); each extent may belong to a different logical volume. To transfer a logical volume to a different group, you cannot simply transfer extents, because that might split the physical volume between the source VG and the target VG.
What you can do is transfer one or more PVs from the source VG to the target VG, with the
vgsplit command. You can specify which PVs you want to transfer, or which LV (but only one at a time). If you specify an LV, it and the other LVs in the source VG must be on separate PVs. The destination VG will be created if no VG exists with the specified name.
vgsplit -n source_group/volume_to_copy source_group target_group
vgsplit source_group target_group /dev/sdy99 /dev/sdz99
You may need to use
pvmove first to arrange for the logical volumes you want to move to be on separate PVs.
If you meant to retain the physical boundaries of the VG and move the data, there's no built-in tool, but you could make a mirror then remove the original.