An early use of division in Fourier space to undo a convolution is <A HREF="https://www.osapublishing.org/abstract.cfm?uri=josa-42-2-127">Fourier Treatment of Optical Processes</A> (1952), by Peter Elias, David S. Grey, and David Z. Robinson. (This paper precedes the paper by Maréchal and Croce cited in the OP.)

<IMG SRC="https://ilorentz.org/beenakker/MO/deconvolution_1952.png"/>

---

Following the OP's and Copeland's lead to Pincherle suggests this 1907 publication <A HREF="http://www.bdim.eu/item?fmt=pdf&id=GM_Pincherle_CW_2_302">Sull'inversione degli integrali definiti</A>. The convolution theorem for Laplace transforms [called "funzioni generatrici" – generating functions] is stated and used to invert the convolution by dividing the transformed functions:

<IMG SRC="https://ilorentz.org/beenakker/MO/deconvolution_1907.png"/>

<sub> From eq. (10), or the equivalent (10'), we immediately find the answer to question number 4. Indeed, equation (d)
$$\frac{1}{2\pi i}\int a(x-t)f(t)dt=g(x)$$
 is equivalent [for the Laplace transforms] to $Gg=Ga\cdot Gf$ or $\gamma(u)=\alpha(u)\phi(u)$, and hence the function $f$ is determined by [the inverse transform of] $\gamma(u)/\alpha(u)$.</sub>