How to switch to offshore banking?

You are already in the banking sector. But now you want to shift to an offshore banking job. For this, you have to get a job in a bank which can post in any other country. You can always try for that. The following ways you can think of.

1. If the bank presently you are working is having a branch in any other country, you can try for getting a post in that overseas bank branch. One of my friends was working in SBI. He tried and got transferred to the SBI branch in Dubai. He worked for more than 10 years there and now he is retired. Similarly, you can also try for a transfer to an offshore bank branch.
2. There are some foreign banks that are having branches in India. You can try for a posting in such banks in India and after getting a job there, you can try for a transfer. HSBC and Stanchart bank are two banks. They have many branches in India and other countries also.

Coming to your other question about the FRM course, the details are as follows,
FRM is Financial Risk Management. Global Association of Risk Professionals (GARP), USA is offering a certificate course in FRM. This is having a very high value among the financial business houses. The course covers all aspects of the finance sector and risks associated with this aspect and the ways and means to handle these risks. There are two parts to this. There is no minimum qualification prescribed for clearing Part 1 in this.But you will be given certificate only after clearing the Part 2 also. FRM certificate is equal to maters degree in almost 10 nations and you will have a better chance to get an appointment in offshore banking. In some other countries this certificate will be treated equal to graduation and that is also good to get a job in offshore banking with your experience,

If interested for the offshore banking job, it could facilitate your future provided you get a job in a reputed nationalised bank having their branches in the foreign countries so that you land a off shore job. If you have sufficient length of experience in your present bank and have accumulated enough knowledge of the different working process of the bank, it would not be difficult for you to have got such a responsibility in other nationalised bank.
However this is one part of your homework and the other crucial aspect is to come closer to the boss of the bank who could evaluate you in terms of your working skills multiplying the business to a higher trajectory. Your consistent performance in your assignment could create a favourable impact ultimately on his mind and as a capacity of a senior banking officials, he can recommend your name to a bank having its branches in the foreign country.
If you have taken some certified diplomas such as Financial Risk Management, Charted Financial Analyst, Certified Financial Planners, Certified Corporate Trust Specialist, Alternative Investment Analyst to raise your efficiency prior to your foreign postings, this would have favourable impact. Ensure that you need to pay attention to one of these certifications while you are in your banking job in the primary stage but be sure these certifications are from the recognised institutions accepted in the Banking Circles.
Once you get a job in a foreign country like USA, Canada, Germany etc representing your nationalised bank, try for a change for the offshore banking job by virtue of your capabilities.

If you are planning to apply for a position in an offshore bank then there are two types of these banks where you can apply. First is the foreign branches of our own Indian banks. Second category is foreign banks.
With your existing experience you can definitely apply for the positions which are following vacant or being advertised by these banks for their foreign assignments but it is to be understood that there is a tough competition for that and you will have to acquire some additional qualifications also.
The most common courses in this connection are certificate in offshore banking, a course in investment banking, portfolio management banking, global insurance aspects etc.
There are some online agencies like Coursera, Unacademy, Alison, Udemy, Olc, Softtrust and many more from where a person can aquire these learnings related to offshore banking.
There are many international transactions that are negotiated by the offshore banking and acquiring these courses will help the person to learn these basics of international banking and compete for foreign assignment.