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"/>

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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 is stated and used to invert the convolution:

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