The phrase "have the law on" refers to having the legal power or authority to prosecute or take action against someone who has committed an offense. There are numerous synonyms that can be used in place of this phrase such as "be within your rights," "possess legal authority," "have jurisdiction," "have legal leverage," "have legal standing," "have legal grounds," or "have legal recourse." These synonyms illustrate the various ways in which one can have the ability to enforce the law against another individual who has engaged in unlawful conduct. Understanding these synonyms can help individuals better express their legal rights and authority in various situations.