  The question whether stellar bars are either transitory features or
long-lived structures is still matter of debate. This problem is more acute for
double-barred systems where even the formation of the inner bar remains a
challenge for numerical studies. We present a thorough study of the central
structures of the double-barred galaxy NGC1291. We used a two-dimensional
multi-component photometric decomposition performed on the 3.6$\mu$m images
from S$^4$G, combined with both stellar kinematics and stellar population
analysis carried out using integral field data from the MUSE TIMER project. We
report on the discovery of the first Box-Peanut (B/P) structure in an inner bar
detected in the face-on galaxy NGC1291. The B/P structure is detected as
bi-symmetric minima of the $h_4$ moment of the line-of-sight velocity
distribution along the major axis of the inner bar, as expected from numerical
simulations. Our observations demonstrate that inner bars (similarly as outer
bars) can suffer buckling instabilities, thus suggesting they can survive a
long time after bar formation. The analysis of the star formation history for
the structural components shaping the central regions of NGC 1291 also
constrains the epoch of dynamical assembly of the inner bar, which took place
$>$6.5 Gyr ago for NGC1291. Our results imply that the inner bar of NGC1291 is
a long-lived structure.
