In the 1990s, he should be/should have been in his forties.

In the 1990s, he should be/should have been in his forties.
 

-This writer is well-known for the power of his words shown in newspaper columns. After graduation from university, he worked as a translator. In the 1990s, he became a columnist. At that time, he should be/should have been in his forties.

I'm guessing at what age he was at that time, which tense should I use?

should have been

There should be no hyphen in "This writer is well-known."
American English speakers don't say 'after graduation from university'. We say 'after graduation from the university.'

Thank you, Rusty.

1. But when referring to even a past period, like just pointing to a time line, won't native speakers say this?;

-The 19th century should be the Victorian Era.

2. Could you tell me the difference between this ''after graduation from the university'' and some quotes of 'after graduation from university' I found in the COCA? Am I correct in saying that the COCA is not a good source of learning English?

No, we would say 'was' instead of 'should be'. "The Victorian Era was in the 19th century," sounds even better, since that era didn't occupy the whole century.

I have never heard anyone in America say 'after graduation from university', even though we readily use 'after graduation from high school' and 'after graduation from college'. I've never used the COCA as a resource, so can give no opinion about it.

Thank you, Rusty. Your words carry a lot of weight.