That’s true. In order to compute the convolution shown above in black I ignored the x-axis from the data (first column in data-Bichsel.txt) because it is not formed by consecutive numbers (otherwise I could not perform a discrete convolution). So, I replaced the first column (9.203623, … , 94867.336) by 1, 2, 3, … , 152.
Anyway, the shape of the true convolution (using as x-axis 9.203623, … , 94867.336), computed with TF1Convolution should be very close to the graph in black. And it is not of all the case, it seems that there are missing parameters.