Recent progress in understanding the assembly history of the Milky Way (MW) is driven by the tremendous amount of high-quality data delivered by Gaia (ESA), revealing a number of substructures potentially linked to several ancient accretion events. In this work we aim to explore the phase-space structure of accreted stars by analysing six M31/MW analogues from the HESTIA suite of cosmological hydrodynamics zoom-in simulations of the Local Group. We find that all HESTIA galaxies experience a few dozen mergers but only between one and four of those have stellar mass ratios > 0.2, relative to the host at the time of the merger. Depending on the halo definition, the most massive merger contributes from 20% to 70% of the total stellar halo mass. Individual merger remnants show diverse density distributions at z = 0, significantly overlapping with each other and with the in situ stars in the Lz − E, (VR, Vϕ) and (R, vϕ) coordinates. Moreover, merger debris often shifts position in the Lz − E space with cosmic time due to the galactic mass growth and the non-axisymmetry of the potential. In agreement with previous works, we show that even individual merger debris exhibit a number of distinct Lz − E features. In the (VR, Vϕ) plane, all HESTIA galaxies reveal radially hot, non-rotating or weakly counter-rotating, Gaia-Sausage-like features, which are the remnants of the most recent significant mergers. We find an age gradient in Lz − E space for individual debris, where the youngest stars, formed in the inner regions of accreting systems, deposit to the innermost regions of the host galaxies. The bulk of these stars formed during the last stages of accretion, making it possible to use the stellar ages of the remnants to date the merger event. In action space (Jr, Jz, Jϕ), merger debris do not appear as isolated substructures, but are instead scattered over a large parameter area and overlap with the in situ stars. We suggest that accreted stars can be best identified using Jr > 0.2−0.3(104 kpc km s−1)0.5. We also introduce a new, purely kinematic space (Jz/Jr-orbital eccentricity), where different merger debris can be disentangled better from each other and from the in situ stars. Accreted stars have a broad distribution of eccentricities, peaking at ϵ ≈ 0.6 − 0.9, and their mean eccentricity tends to be smaller for systems accreted more recently.