Frankham admitted CPO oversold 1,686 shares ahead of October's vote on whether to hand back the freehold of Stamford Bridge to Chelsea, a vote the club nevertheless lost to prevent them being able to move to a new stadium.
The group which spearheaded the campaign against the Blues' plans - 'Say No CPO' (SNCPO) - last week urged their supporters to block the resumption of the sale of shares at Friday's annual general meeting unless oversold shares were rescinded.
But the man who succeeded Richard King as CPO chairman in the wake of October's stormy extraordinary meeting was adamant it was not possible to render them void.
Frankham said in a message to shareholders: "The CPO board was not aware it was not properly authorised to issue those shares.
"However, company law is clear that the issue of the 1,686 shares was still valid and that the CPO board does not have the ability to disenfranchise or rescind the issue of those shares whether it wants to or not."
He added: "I have also been asked to confirm that the CPO board unanimously recommend that shareholders vote in favour of all of the resolutions to be proposed at the AGM, as the CPO board members intend to do in respect of their own shareholdings.
"We accept that people feel mistakes have been made in the past but - with your backing - we are aiming to address these concerns.
"But I must emphasise that all members of the board feel the same way. We have nothing to hide.
"(SNCPO sympathiser) Gray Smith, who became a director of CPO following his raising of objections at the October EGM, is a senior corporate lawyer, and has agreed with the above legal analysis concerning the share issue."
SNCPO also urged shareholders to vote off the two remaining directors from October's three-man board, Bob Sewell and non-shareholder Rick Glanvill, claiming the latter's membership was illegitimate.
Frankham said: "Rick Glanvill is standing for re-election to the CPO Board at the AGM.
"He is not employed by Chelsea FC. He is a freelancer and, while he has done some work for Chelsea, he is still independent of the club.
"His status does not breach the articles of association of CPO, which merely prohibit a director of Chelsea FC or a person involved in the management of CFC from being a director of CPO.
"There is no legal requirement, whether in the CPO articles of association or otherwise, for a CPO director to hold CPO shares."
