This kind of integration usually sounds simple but then is not so simple at all (Note that questions here usually lack what I would call "Requirements" which basically tells you the requestor has not thought about what is supposed to be achived.).  For all I can tell, you have these options:

1. Search for an existing solution that synchronizes work items and the data of the other vendor; there are solutions around that you could look into
2. Create a custom solution - Very expensive, unclear requirements and the usual issue is the UI and if it might even be doable

I would suggest to look into 1. Option 2 is likely more expensive then using an existing of the shelve solution.