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.
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