Biometric recognition systems are security systems based on intrinsic properties of their users, usually encoded in high dimension representations called embeddings, which potential theft would represent a greater threat than a temporary password or a replaceable key. To study the threat of embedding theft, we perform spoofing attacks on two behavioral biometric systems (an automatic speaker verification system and a handwritten digit analysis system) using a set of alignment techniques. Biometric recognition systems based on embeddings work in two phases: enrollment - where embeddings are collected and stored - then authentication - when new embeddings are compared to the stored ones -.The threat of stolen enrollment embeddings has been explored by the template reconstruction attack literature: reconstructing the original data to spoof an authentication system is doable with black-box access to their encoder. In this document, we explore the options available to perform template reconstruction attacks without any access to the encoder. To perform those attacks, we suppose general rules over the distribution of embeddings across encoders and use supervised and unsupervised algorithms to align an unlabeled set of embeddings with a set from a known encoder. The use of an alignment algorithm from the unsupervised translation literature gives promising results on spoofing two behavioral biometric systems.