It is the established policy of the Government that one cannot migrate from department to another department of the Central or a State Government without the knowledge and permission of the parent department. This includes autonomous undertakings, Government departments, public sector undertakings and major Government aided institutions. This is so ever since the British times. In fact I know cases where disciplinary action was taken by the parent department for defying this rule.
Is this a valid policy in a free country? This has to be examined from the point of view of either side. An employee in an organisation, besides getting salary for the work for the employer also benefits by learning through experience. If there is a fast turn over of employees, the employer is deprived of experienced staff. Thus some reasonable restriction is justified to protect the interests of the employer.
On the other hand such a policy in the extreme amounts to bonded labour. This is particularly so if the employer is an all-pervading monolith like the Government.
In short you have no choice but to stick to your parent department and thank your own stars that no further disciplinary action is taken against you.
In any case one does not know whether such a policy does not infringe upon one's Constitutional rights.
Years ago it was the policy of the Government that an application from a Government servant for a passport would not be entertained without a No Objection Certificate from the parent department of the Governemt Servant. Some 40 years ago this requirement was challenged in the Supreme Court. The Supreme Court struck down this requirement saying that the right to a passport was a fundamental right guaranteed under the Constitution. An NOC is still required. But the Government will give it as a matter of routine.
So far no one has challenged this 'through proper channel' rule in a court of law, to the best of my knowledge. Other Forum members may be able to throw more light on this issue.