"Certificate of completion of the 3-year program at the high school for career training"

Our high school has the grade 12 and grade 13 completion certificates, so I am familiar with 2 diff. programs in one HS.
BW, Nancy

In the USA students graduate from High School. They do receive certificates, but that is not included in their resume. Probably the program would be the equivalent of BOCES, but that might be too large a jump, since the program described seems to be incorporated in the Gymnasium curriculum. I think vocatinal is better than career here.

The choice here seems to be between describing the program in terms of what an English or American client can understand, or simply rendering the German, without allowing for differences in the educational programs of the countries.

Certificate of completion for three-year vocational (extended) high school program.

Integrating uel's answer to your last question with the vocational context seems to me tofit the bill, but check for yourself and decide.

Cheerio,
Dierk