Difference between buddhasasana and buddhadhamma Is it correct to say that the buddhasasana (the teaching of the Buddha) is conditioned and impermanent in contrary with Dhamma itself which is unconditioned and permanent.
Is it correct to say that the buddhasasana (the teaching of the Buddha) is conditioned and impermanent in contrary with Dhamma itself which is unconditioned and permanent.


No. 

Sasa = verb (Teach)

Sasana = noun (Discipline&Doctrine;teaching)

Dhamma = Discipline&amp;Doctrine

BuddhaSasana = Discipline&amp;Doctrine of the Buddha

Sutta. Tī. Pā. Udumbarikasuttaṃ:


  Let a sensible person come—neither devious nor deceitful, a person of integrity. I teach (aham-anusāsāmi) and instruct them doctrine (Dhamma). By practicing as instructed they will realize the supreme end of the spiritual path in this very life, in seven years. 
  
  Ahaṃ  pana  nigrodha  evaṃ  vadāmi etu viññū puriso asaṭho amāyāvī   ujujātiko   ahamanusāsāmi   ahaṃ   dhammaṃ  desemi  yathānusiṭṭhaṃ tathāpaṭipajjamāno     yassatthāya    kulaputtā    sammadeva    agārasmā anagāriyaṃ   pabbajanti   tadanuttaraṃ  brahmacariyapariyosānaṃ  diṭṭhe  va  dhamme sayaṃ   abhiññā   sacchikatvā   upasampajja   viharissati   satta  vassāni .


Dhamma in your context is a part of Buddhasasana. To consider abot it, the  Buddha taught in Sutta. Ma. Mū. Cūḷasaccakasuttaṃ:


  'Form is inconstant. Feeling is inconstant. Perception is inconstant. Fabrications are inconstant. Consciousness is inconstant. Form is not-self. Feeling is not-self. Perception is not-self. Fabrications are not-self. Consciousness is not-self. All conditioners are inconstant. All phenomena (Dhamma) are not-self.' This, Aggivessana, is the way in which I discipline my disciples; this part of my instruction is generally presented to my disciples."
  
  rūpaṃ  bhikkhave aniccaṃ   vedanā   aniccā  saññā  aniccā  saṅkhārā  aniccā  viññāṇaṃ aniccaṃ   rūpaṃ   bhikkhave   anattā   vedanā   anattā   saññā  anattā saṅkhārā    anattā   viññāṇaṃ   anattā   sabbe   saṅkhārā   anattā sabbe   dhammā  anattāti  evaṃ  kho  ahaṃ  aggivessana  sāvake  vinemi evaṃbhāgā ca pana me sāvakesu anusāsanī bahulā pavattatīti.


By above Sutta:


All aggregates are conditioners (each others) because they are same inconstant.
All aggregates are Dhamma because both of them are same not-self.
So some Dhamma, Nibbāna and Sammati, is not conditioned and not inconstant.

-Nibbana is not conditioned, not constant, and not-self. It is reality which never arising, no aggregates at all. It's real because it is the opposite of all aggregates, not based on any aggregates. People can access Nibbana by the complete Vipassana, Magga.

-Conception, Sammati, is not conditioned, not constant, and not-self. It is unreal and never arise, just imagination based on aggregates. Every people can access Sammati. Some people can use Sammati in meditating Lokiya-Jhāna to avoid craving in aggregates, but it is impermanent avoidance because minds create Sammati from thinking of aggregates, therefore it is possible to crave aggregates again in the future, so Sammati is not the perfect opposite of aggregates. However Lokiya-Jhāna is still important for Vipassanā meditation.