Is it permissible for a mother to conceal her drug-addicted son, who confessed to her that he stole, and asked her to deny it in front of people?

A child must be prohibited from stealing and drug addiction. Repentance involves abandoning the sin, regretting it, resolving not to return to it, and restoring rights to their owners. If the child repents and restores rights, then they must be covered (their sin concealed). Otherwise, it is not permissible to cover for them unless there is a fear of significant harm.