His first big break in journalism came when he was promoted to writing obituaries for the local newspaper.
Why that position is "writing", I think it must be "write".
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It changes the meaning
Promoted to [writing obituaries]
He was promoted and after the promotion writes obituaries.
Promoted [to write obituaries]
He was promoted specifically so that he could write obituaries.
Here, "to write obituaries" is the reason for promotion. Previously, there was no reason given and "writing obituaries" could have been a coincidental job in his role.