Does change in salary (with Company A) effects the H1B Transfer Process with company B

Changes to your salary by your current employer have no impact on your future application for another employer. Depending on your current circumstances, you may be able to start working for the new employer once the new H-1B petition is filed, under the "portability" provisions of AC21. You should consult with an immigration attorney before making any job changes.

The wages that you receive with your current employer will not have any impact on the H-1B petition filed by your prospective employer.

If the salary hike is accompanied by a change in job title, there could be a relevant issues related to the LCA/prevailing wage at A. However, I doubt that A would be trying to put themselves in some sort of violation over your H-1B (i.e. not paying you enough according to the law) in order to hurt you. It seems more likely they want to retain you and thus the raise. However, if you're concerned about the intentions of Company A (that they know you're transferring and seek to harm you), I would get a meeting with Company B's immigration attorney if they have one.

Changes within one company do not affect the other.

The salary 'hike' shouldn't be a problem. But, do NOT start working for B until AFTER the transfer to B is approved.