Generally, the welder is certified by the employer.
Under the auspices of the AWS structural welding codes and ASME B&PV Code, as well as military welding standards, the employer is responsible to ensure their welders are properly qualified.
The qualification part of the process is when the welder takes the performance test consisting of a plate or pipe assembly in the appropriate test position and using the specified welding process and electrode/filler metal combination. The welder must follow a written welding procedure specification, i.e., a recipe to make the required weld. If the welder passes the applicable soundness tests, i.e., guided bend tests, radiographic examination, or a break test in the case of a fillet weld, the employer (or laboratory) completes the welder performance test record with the test variable and test results. The employer (a fabricator, erector, etc.) then signs the certifying statement at the bottom of the test report.
The employer is responsible for the work performed by the employee. It is reasonable to expect the current employer to certify, i.e., signs the certifying statement, attest to the fact the welded is properly qualified. If the employer is not willing to accept responsibility for the welder's work, why should an owner allow the welder to work on the project?
Qualification is the responsibility of the employer. Whether the welder tests on the premises of the employer's facility, takes the test at a third party's facility, or the welder was previously qualified by a previous employer, the current employer is still responsible for certifying the welder is qualified.
The welder can be tested in accordance with AWS D1.1, D1.2, D1.6, etc. by the employer, under the employer’s supervision, or by a third party. Regardless of the code tested to, it is the employer that signs the certification statement attesting to the fact the welder has been properly qualified.
An alternative is for the welder to be tested by an AWS Accredited Test Facility, in which case the AWS issues a welder certification. Currently the test record is not a complete report, i.e., it doesn't list all the test information. There is no space for the current employer to cosign the test repot. As such, the employer is not attesting to the fact the welder is properly qualified. That being the case, why should an owner accept the AWS issued "certification" if the current employer will not sign the paperwork? There appears to be a slight conflict between the AWS ATF program, what the welding code requires, and the employer's legal responsibility under the code. However, it is money making machine for AWS.
Most welding standard, AWS included, revokes the welder's qualifications if no welding using the process for which qualification is held for a period of more than six months.
Best regards - Al