Yes, a Trademark obtained by sole proprietorship can be continued as the same even if it is converted as a One Person Company or Private Limited Company. For that all you have to do is File form TM P or TM M with supporting documents, with prescribed fees. You might need to attach a letter explaining your problem with verification from the person whose name is there on the Trademark certificate.
The Registry will further verify your application and Officer-in-charge may seek any clarification or supporting documents to prove the genuineness of the application. If he is satisfied with your clarification, he will approve of changing the type of business structure.