SSIS Package fails to "Transform File and create output file"

I have an SSIS (2012) package which was written by one of the developers. I've been tasked to with fixing the error. Each time the package is run I receive the following three messages indicating the Write Output File [339] produced errors.

Transform File and create output file:Error: Write Output File failed the pre-execute phase and returned error code 0xC020200E

Transform File and create output file:Error: Cannot open the datafile "\\servershare\folder\file"

Transform File and create output file:Warning: Access is denied.

I have tried granting full control to the folder share to myself, the SQL Agent account, and the SQL Services account. Whether I run the package as myself or as a service account I receive the error messages.

I'm not seeing any more details in the SQL Server error logs or the Windows Event logs.