  We performed a theoretical investigation on the mixing-length parameter
recovery from an eclipsing double-lined binary system. We focused on a syntetic
system composed by a primary of mass M = 0.95 Msun and a secondary of M = 0.85
Msun. Monte Carlo simulations were conducted at three metallicities, and three
evolutionary stages of the primary. For each configuration artificial data were
sampled assuming an increasing difference between the mixing-length of the two
stars. The mixing length values were reconstructed using three alternative
set-ups. A first method, which assumes full independence between the two stars,
showed a great difficulty to constrain the mixing-length values: the recovered
values were nearly unconstrained with a standard deviation of 0.40. The second
technique imposes the constraint of common age and initial chemical composition
for the two stars in the fit. We found that $\alpha_{ml,1}$ values match the
ones recovered under the previous configuration, but $\alpha_{ml,2}$ values are
peaked around unbiased estimates. This occurs because the primary star provides
a much more tight age constraint in the joint fit than the secondary. Within
this second scenario we also explored, for systems sharing a common
$\alpha_{ml}$, the difference in the mixing-length values of the two stars only
due to random fluctuations owing to the observational errors. The posterior
distribution of these differences was peaked around zero, with a large standard
deviation of 0.3 (15\% of the solar-scaled value). The third technique also
imposes the constraint of a common mixing-length value for the two stars, and
served as a test for identification of wrong fitting assumptions. In this case
the common mixing-length is mainly dictated by the value of $\alpha_{ml,2}$.
[...] For $\Delta \alpha_{ml} > 0.4$ less than half of the systems can be
recovered and only 20% at $\Delta \alpha_{ml} = 1.0$.
