There's a few things wrong with that statement...
- The 2610 will never work with NT mapping
- Unlock codes are not transferable between Garmin GPSs, each code is tied to a specific GPS unit and one version of the mapping data
- I can't see how you could buy NT mapping for a 2610 and be provided with an unlock code
- The 660 should have come with pre-installed mapping and be eligible for registration of a myGarmin account, this would reveal the unlock code for that device/mapping combination.
Whilst OpenStreetMap data will work with both your 2610 and the 660 it won't provide full functionality on the 660. It'll navigate OK, maybe slightly differently to Garmin/Navteq mapping data, not necessarily worse, just differently. There will be certain, not critical, functions that won't work though.
The alternative is to buy a Lifetime subscription for the 660 from
Handtec, you will need a myGarmin account to activate and use this for updates though. Reading between the lines I'm assuming you don't have one of these though. Maybe your 660 is 2nd hand and the seller didn't, or wasn't able to, provide details or de-register the Zumo with Garmin
Garmin should be able to help get the device registered to you all the same, they try to contact the previous owner and if they don't get a response after a few days will de-register the Zumo allowing you to register it in your name. Usually they are pretty helpful.
Of course, if you bought the thing in a pub off a shady geezer then Garmin will quite rightly block you from any updates and have nothing to do with you.