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At room temperature, bulk La$_{7/8}$Sr$_{1/8}$MnO$_3$ is in the dynamicJahn--Teller O$^*$ phase, but undergoes a transition to a static, magneticallyordered Jahn--Teller phase at lower temperatures. Here we study a $6$ unitcells thin film of this compound grown on SrTiO$_3$, resulting in smallcompressive strain due to a lattice mismatch of $\lesssim 0.2\%$. We combineX-ray absorption spectroscopy with multiplet ligand field theory to study thelocal electronic and magnetic properties of Mn in the film. We determine the Mn$d_{3z^2-r^2}$ orbital to be $0.13\;\text{eV}$ lower in energy than the$d_{x^2-y^2}$, which is a disproportionately large splitting given the smalldegree of compressive strain. We interpret this as resulting from the strainproviding a preferential orientation for the MnO$_6$ octahedra, which arestrongly susceptible to such a deformation in the vicinity of the phasetransition. Hence, they collectively elongate along the $c$ axis into a staticJahn--Teller arrangement. Furthermore, we demonstrate the strongly covalentcharacter of La$_{7/8}$Sr$_{1/8}$MnO$_3$, with a contribution of nearly $50\%$of the one-ligand-hole configuration $d^{5} \underline{L}^1$ to the groundstate wavefunction. Finally, we find the system to be in a high-spinconfiguration, with the projection of the local magnetic moment on thequantization axis being about $3.7\;\mu_{\text{B}}/\text{Mn}$. We show,however, that the system is close to a high-spin--low-spin transition, whichmight be triggered by crystal field effects.

Strain induced stabilization of a static Jahn-Teller distortion in the O$^*$-phase of La$_{7/8}$Sr$_{1/8}$MnO$_3$