The original ePub2 file should have passed an ePub check, such as is available (freely) from pagina.
You should then check the resulting ePub3 directory and if all OK, edit any files as required (and check again!)
Note, that the ePub checker will create an ePub file for you (if there are no warnings or errors).
3Pub Assist is free to use, but you can also make a donation when purchasing.
If you choose not to donate, the required payment details will not be required.
You may not distribute the software to others:-)
If you have trouble converting your ePub2 file, I will be happy to consider modifying the code, but you will need to email me the ePub2 file for testing purposes.