Fragomen is certainly a well known and established corporate immigration firm. That part is not in dispute. The exposure you will get will stand you in good stead for other immigration firms.
However, working for Fragomen in the UK is certainly an interesting experience. First and foremost you will be working under a lot of pressure. Monthly billing targets are the most important factor. If you don't meet them, then be prepared to face a roasting by your line manager. They are not sympathetic.
Working at Fragomen is ok for a short period as they will introduce you to the immigration work. However, they have a large turnover of non lawyers to rival firms such as PwC, EY and KPMG. Why? Well the money and benefits are far better but also they have a better working environment and do not have a blame culture which Frags has. You would have guessed that Frags would have realised this by now but sadly not. Will they ever?
Also, the only way to progress is to become a qualified lawyer. They recruit internally for training contracts every year with around 4 positions available. If you can't qualify then you will face a brick wall. Period!
Good exposure to corporate immigration
Blame culture, support staff such as Paralegals and Coordinators treated as second class employees