Undertake investigation in Anchorites properly (6,4)

I believe the answer is:

search into

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'undertake' is the definition.
I don't know anything about this answer so I can't tell whether it can be defined by this definition.

'investigation in anchorites properly' is the wordplay.
'investigation' becomes 'search' (search is a kind of investigation).
'anchorites properly' becomes 'to' (I can't justify this - if you can you should believe this answer much more).
'search'+'in'+'to'='SEARCH INTO'

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I've seen this clue in the Sydney Morning Herald.

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