A prosthetic spinous process cross-link implant for the replacement of a posterior vertebral element. The implant includes a cross link body member with a pair of adjustable link arms connected to the cross link body to size the implant to specific anatomical configurations. The implant includes a rod clamp that is spring loaded to a forward position such that capturing a spinal rod on to the adjustable link arms to achieve a snap on effect thereby increasing the ease of installation. A plurality of spinous process cross-link implants can be assembled as a kit wherein the set includes a group of spinous process type yokes and bridge type yokes each group including both fixed and variable sized implants.