verstand es in einer Weise -- help with German sentence

[sedmont]

The German sentence below was written in 1950.

I don't know if I've understood the red German phrase below and translated it properly into English. Thank you very much for any assistance.
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Smith verstand es in einer Weise, auf die Gedanken und Empfindungen jedes einzelnen Menschen, auf dessen besondere Lebenslage oder Lebensaufgabe so einzugehen, daß sich immer rasch ein echt menschliches Vertrauen entwickelte.

Smith understood how to so enter into the thoughts and feelings of every individual person, into the person's particular life situation or life tasks, that a genuine human trust always quickly developed.