Hey Alex,
It seems the cause is that we activated the software under one account but using under the other.
Yes, this is by design. We didn't want to require admin privileges or UAC elevation to activate, thus the activation data is stored locally for each user. You can activate within each user account on the computer without limitation.
You can solve this problem a few ways. One way is to store the product key used for activation in a place that both your admin app and the LocalSystem app can access (e.g. in the registry). Then the service can check if it's activated, and if not use CheckAndSavePKey(), then Activate() to activate it.
Another option is to have the admin app communicate directly with the service using named pipes. The service does all the activation work and reports back to the admin app.
Is any way with LimeLM when I can activate the product under Administrator but this activation will work under the other account?
Not unless you use the methods I just described. We're considering making this easier for special cases like yours.