Synonyms for “passing the buck”?

What would be a better replacement for the informal phrase “passing the buck” (ie. shift responsibility for something to someone else)?

I am in need of a single-word verb that captures the all-too-familiar bureaucratic practice of referring endlessly.

“Refer to” is too neutral of a meaning; it lacks the hypocrisy inherent in “passing the buck”.

“Defer to” implies a responsible act, whereby the referrer is conceding their limitations.

“Abrogate” is open-faced shirking of responsibility - whereas I am after the lazy bureaucratic practice of “passing the buck”.

EXAMPLE:

A comes to B with a problem. B is lazy and doesn’t feel like putting in the work to solve it, so they ______ to another department.

How about delegate?

to give a particular job, duty, right, etc. to someone else so that they do it for you:

• As a boss you have to delegate (responsibilities to your staff).
• Authority to make financial decisions has been delegated to a special committee.

[Cambridge English Dictionary]

shuffle sth off

to get rid of something unwanted, usually by giving it to someone else:

Ex. "The local authority may then try to shuffle these responsibilities off onto another authority." [emphasis mine]

Cambridge Online Dictionary

A phrasal verb, and considered "literary"**, it fits the intended usage well.

A comes to B with a problem. B is lazy and doesn’t feel like putting in the work to solve it, so they shuffled it off (on)to another department.

In some circles, it has higher register than 'pass the buck", but it might also be a "cross-the-pond" thing.