There are two ways of migrating from one government job to another. One is with break of service and the other is with continuity of service. I presume that you want to migrate with break of service. Basically you can resign from one job and join the other one. But generally when you go from one government job to another government job you will be required to apply for the new job through your present employer. If you had not done so, your new employer may require you to get a No Objection Certificate from the old employer.

What is the problem you facing. Do not make it a riddle or question paper

Act in accordance with service rules applicable to your designation in your establishment.

If you wish you attach/post the service rules.

Erase names/logo/address/phone number etc to maintain the confidentiality.