Question regarding Part-time H1b to Full-time H1b

[TNG]

Recently I got h1b on part time job, but now the company wants me to be full time employee.

Do I have to refile for H1b? or does it counts as transfer?

If I decide to move into new company which also giving me options for either Full-time or part-time employee. Do they have to file for H1b? how does it work?

Is it just LCA which needs to be updated or I have to go through entire process again?

[kabkaba]

Recently I got h1b on part time job, but now the company wants me to be full time employee.

Do I have to refile for H1b? or does it counts as transfer?
If previous petition was filed as a part-time petition, the employer will have to file amendment along with new LCA.

If I decide to move into new company which also giving me options for either Full-time or part-time employee. Do they have to file for H1b? how does it work?
There is no option possible. It is either full-time or part-time depending on the way petition is filed. They will need to file a petition using previous petition's cap number. It is just like any other petition.

Is it just LCA which needs to be updated or I have to go through entire process again?

See above.