  Asteroseismology provides a unique opportunity to probe the interiors of
evolved stars and constrain their internal rotation. The correct reproduction
of the core rotation evolution is key to understanding the internal processes
involved in low-mass stars. We explore the efficiency required to reproduce the
behaviour of the transport of angular momentum (AM) in view of asteroseismic
constraints. We computed a series of models and investigated an updated AM
transport by including a time-dependent extra viscosity related to the AMRI. We
compared our predictions to the asteroseismic measurements of the core and
surface rotation of a sample of SGB and RGB stars. We confirm that a
time-dependent additional viscosity is required to reproduce the general
behaviour of the core rotation rate along evolution. We show that it results in
stronger Li and Be depletions for low-mass stars over evolution. We confirm
that predicted Li abundances at the RGB bump by classical models, commonly used
as references, cannot reproduce the Li depletion along the MS and evolved
phases of stellar evolution. We show that the observed amount of Li of stars
less massive than 1Msun leads to a discrepancy between model predictions and
observations at the RGB bump. We show that a semi-parametric model can
reproduce the rotational behaviour along the first phases of evolution well,
with the exception of the sharp transition observed during the SGB phase. This
suggests that two distinct transport processes may be involved. The processes
required to transport chemicals during the MS, and AM until the RGB phase
impact the Li depletion all along the evolutionary duration. A good prediction
of the Li abundance at young phases places strong constraints on the predicted
one at more evolved phases. It also impacts the threshold that defines Li-rich
giant stars, showing that classical models tend to overestimate its value.
