N.M. Stat. § 63-1-28

Shares of the capital stock of any railroad corporation shall be personal property, and may be transferred, by endorsement, by the signature of the proprietor, or his attorney, or legal representative and delivery of the certificate; but such transfer shall not be valid, except between the parties thereto, until the same shall have been entered upon the transfer book of the corporation so as to show the names of the parties by, and to whom, transferred, the number or designation of the shares and the date of transfer: provided, no stock shall be transferred upon the transfer book of the corporation until all previous assessments thereon shall have been fully paid in, nor shall any such transfer be valid except as between the parties thereto, unless at least twenty percent shall have been paid thereon, and certificates issued therefor, and the transfer approved by the board of directors, except by consent of the board of directors.