H1b amendment question

[cyrax]

Hello ,

 

I have been working with a client X for about an year now with job title as Telecommunication engineer under SOC: 17-2072 Electronics Engineers, Except Computer... company A was holding my H1b

 

Client X removed company A from their preferred vendor list due to some ethical violation and gave me an option to transfer to company B , i agreed to move to company B

 

Company B started my H1B transfer under premium processing , H1b transfer was approved for 3 yrs

 

I am still with same client X with no break in employment however i have realized that company B filed my transfer with incorrect job title as computer system analyst SOC:15-1121 Computer Systems Analysts

 

I am not comfortable with this change since i know nothing about computer system analysts and my area of expertise and knowledge is in completely different field i .e telecommunication. Company B wants to start Green card process for me right now however they are reluctant to file an amendment to correct the job title which was their mistake initially. 

 

They claim that job title makes no difference on Green card process or anything, i have also traveled outside the country after my h1b transfer and i was not asked anything about my job title at the port of entry... however since i travel to Canada often i fear this might put me in trouble in future... 

 

Can any one please guide me if i should insist them further to amend H1b before green card or leave everything as is till my next h1b renewal?

can i travel or drive to canada and be back in US while amendment is in process? If they agree on doing that.