Looks like Motorola split into two companies in 2011, with shareholders being given shares in each of the two new companies (Motorola Mobility and Motorola Solutions). Large companies like this tend to appoint a third-party registrar that looks after their share register, so I'd suggest starting with contacting the share registrar for both companies, providing your details (and your parent's address) and asking if they can help.
I cannot find the details for Motorola Mobility, but for Motorola Solutions the contact info is here -
https://investors.motorolasolutions.com/stock-ownership/stockOwnership/default.aspx