Specific verb for "training an apprentice"?
Solution 1:
When this has happened in my professional experience, we always called it "transfer of knowledge" or "knowledge transfer".
This certainly doesn't get the sense of transferring the responsibility, but that is implied: the person receiving the knowledge would be the "go to" person for that area of work.
Solution 2:
Does "mentor" fit the bill?
v. men·tored, men·tor·ing, men·tors Informal
v.intr.
To serve as a trusted counselor or teacher, especially in occupational settings.
v.tr.
To serve as a trusted counselor or teacher to (another person).
Solution 3:
I can't think of a word, but there is this idiom: show the ropes.
The Free Dictionary says:
show somebody the ropes
to explain to someone how to do a job or activity : The new secretary started today so I spent most of the morning showing her the ropes.
Solution 4:
There is a verb but it's not commonly used, induct:
to formally or ceremoniously install in an office, position, etcetera.
to introduce into (particularly if certain knowledge or experience is required, such as ritual adulthood or cults).
to draft into military service.
to bring in as a member.
It's more commonly used as a noun, induction:
The induction you will receive in your local department/institution will enable you to:
- Meet your key colleagues.
- Find your way around your workplace.
- Understand your terms and conditions of employment.
- Understand your role, key responsibilities and how you fit into your department/institution.
An induction meets one of your requirements as it is almost always done at the start of someone's employment, however it does not imply any hand-over of responsibilities, only that of giving an understanding to a new employee.
Solution 5:
English has the verb "apprentice". In my experience, this is most commonly used in the intransitive form:
to serve as an apprentice ("She apprenticed with Bob in her youth.")
However, there is also a transitive counterpart:
to set at work as an apprentice; especially : to bind to an apprenticeship by contract or indenture ("Why Paul Revere's father apprenticed him instead of sending him to college.")
Perhaps that fits more what you're looking for.