Is there any free software that can convert Cadence files (.dsn, .opj, .brd) into Eagle CAD files (.brd, .sch)?
Importing from different CAD packages often has issues.
There are three main parts: schematics, libraries (containing schematic symbols and PCB footprints) and PCB layout.
CAD packages can import them as individual's but do not necessarily import all three as a linked package. This can cause issues for future maintenance of the boards and manufacturing issues due to footprint's not being verified and validated fully during the translation.
A safer and often shorter in the long term approach is to duplicate the library parts and verify all symbols and foot prints, followed be re-entering the schematics, (this will be trivial once all the parts are in the library) and re-laying out the PCB using the existing PCB files as a guide.
This is the only way you can be certain all parts used are correct, and you have not created or lost any artefacts during the PCB importation process.
There is no tool for the purpose , as of now. You have to rework.