I have integrated latest Facebook android sdk (Sdk 4.0). This is the code I have added in my onCreate method.
FacebookSdk.sdkInitialize(this.getApplication
I have not tested this myself but what I think you can do is to get the AccessToken from the LoginResult object in the onSuccess method of the callback.
So: AccessToken accessToken = loginResult.getAccessToken();
Then you would save this accessToken down by saying:
AccessToken.setAccessToken(accessToken);
Then when you call AccessToken.getAccessToken, it should return the accessToken you have saved.