If you can show that faulty installation was the cause of the mold problem your parents could definitely sue the installer for damages related to mold, and possible to his health problems.
To prove negligence (negligent installation), you would have to show that the installer did not live up the ordinary standard of care for an AC installer. Basically, it is a case where if it was incorrectly installed through his own error, you would win. The issue is showing that it was installed incorrectly, and not that something changed over time through no fault of the installer, and that it did in fact cause the mold.
But yes, there is no reason your parents could not sue and win. The installer most likely has insurance to cover these things, so you shouldn't have trouble finding a lawyer to represent them.
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