inverse laplace transforms of shifts

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A simple implementation using the local heaviside function (see also generalized functions) is written in this question, and is such that:

var('t s')
u=piecewise([[(0,3),0],[(3,infinity),exp(-2*(t-3))]], var=t)
F(s) = u.laplace(t,s);
InverseLaplace(F, s, t)

produces $\newcommand{\Bold}[1]{\mathbf{#1}}t \ {\mapsto}\ e^{\left(-2 \, t + 6\right)} H\left(t - 3\right)$.

I guess Maxima can't do it.

sage: inverse_laplace?
def inverse_laplace(ex, t, s):
    r"""
    Attempts to compute the inverse Laplace transform of
    ``self`` with respect to the variable `t` and
    transform parameter `s`. If this function cannot find a
    solution, a formal function is returned.

(%i1) display2d:false;
(%o1) false
(%i2) f(s):=%e^(-3*s)/(s+2);
(%o2) f(s):=%e^-(3*s)/(2+s)
(%i4) ilt(f(s),t,s);    
(%o4) 'ilt(%e^-(3*s)/(s+2),t,s)

Does that answer things? If you want to file an enhancement request to Maxima, please do, maybe it's not so hard for them to implement; however, presumably there are arbitrarily hard ones like this that no system could do...