How to shift from convolution product to the scalar product with arrays?

hy guys, hope you are doing well

I know that the product of the 2 signals in the frequency domain is equal to the Fourier transform of their convolution in the time domain

Y(f)= x(f). h(f)= fft( conv( x(t), h(t))

However, I tried to do the same in 2d with array and I didn't get the same result, i expected that the plot in subplot(244) would be equal to the plot in subplot(247)

Any idea how to fix it ?

Thank you in advance

code:

clear all

clc

n=3;

m=5;

a=rand(n,m)

b=rand(n,m)+1i*rand(n,m);

c=conv2(a,b);

subplot(241)

pcolor(abs(a))

title('a')

subplot(242)

pcolor(abs(b))

title('b')

subplot(243)

pcolor(abs(c))

title('c=conv2(a,b)')

subplot(244)

pcolor(abs(fftshift(fft2(c,n,m))))

title('fft2(c)')

subplot(245)

tfa=fftshift(fft2(a))

pcolor(abs(tfa))

title('tfa')

subplot(246)

tfb=fftshift(fft2(b))

pcolor(abs(tfb))

title('tfb')

subplot(247)

tfab=tfa.*tfb;

pcolor(abs(tfab))

title('tfa.*tfb')