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Create your own apex REST webservice class which will convert the lead record into Account, Contact and Opportunity. Here is the sample code for writing the logic for converting lead process - http://www.salesforce.com/us/developer/docs/apexcode/Content/apex_dml_convertLead.htmNow you have created a custom REST API class (http://www.salesforce.com/us/developer/docs/apexcode/Content/apex_rest_code_sample_basic.htm ) which will convert your lead, now call your REST API class in your code to convert lead.
Thanks,http://karanrajs.com"/services/apexrest/yourRestClassName/leadId"