halacha theory - Why does a fresh convert retain his property?

It seems pretty obvious that a convert keeps his property. It is also Halachicly valid - a convert does not re-acquire his property back after conversion (see Mishnah_Peah.4.6 or Mishnah_Challah.3.6 thanks Heshy).

But why? Here's how I reason: We hold that (Yevomos 48b):

גר שנתגייר כקטן שנולד דמי
(a convert is like a newly born child)

A convert "receives" a new, Jewish soul. Therefore he loses his association with his "former life", for example, his affiliation with all his blood relatives¹.

While a Gentile, he had property and now he's a new man, so I would assume his property is no longer associated with his former soul and is [a sort of] Hefker.

So how come that he "changes a soul" but keeps all his possessions?

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^{1 except for his biological kids for the Mitzvah of Pru Urvu} .