The phrase "this shift to" is correct and can be used in written English.
It is often used to introduce a change or transition in a topic or idea. Example: "This shift to renewable energy sources has been a major focus for the government in recent years."
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Communicating this shift to listeners is equally crucial.
Siegel attributes this shift to "an ethical change in society".
He attributed this shift to Mumbai's prohibitively expensive property prices.
This shift to a commodity market, however, carries risks for consumers.
This shift to a specialised intervention program explicitly recognises the gap left by earlier governments.
This shift to bonds could be another signal that investors fear a further decline in stocks.
This shift to high-stakes testing has not happened without controversy.
To accommodate this shift to the right, the Chancellor enacted a more nationalistic foreign policy.
"This shift to clean, safe energy choices will help fight global warming and ensure a stronger economy and healthier communities".
And now we've seen this shift to aligning with Islamic State, even calling themselves Islamic State's west African province.
This shift to "fight or flight" mode is automatic, but that doesn't mean it's wholly out of your control.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com