An early use of division in Fourier space to undo a convolution is Fourier Treatment of Optical Processes (1952), by Peter Elias, David S. Grey, and David Z. Robinson. (This paper precedes the paper by Maréchal and Croce cited in the OP.)
Following the OP's and Copeland's lead to Pincherle suggests this 1907 publication Sull'inversione degli integrali definiti. The convolution theorem for Laplace transforms is stated and used to invert the convolution:
