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It is not contrary to the Criminal Code to broadcast a telephone call on a speakerphone without the other caller's consent.
If there is litigation regarding this matter, the lawyer would or could be a witness and would be unable to act as counsel.
If you are involved in a civil dispute and need to retain a civil litigation lawyer, your province or territory's law society's lawyer referral service can provide you with the names of local lawyers who can act as your advocate.