  We classify the pairs of group morphisms $\Gamma \rightarrow {\rm Spin}(7)$
which are element conjugate but not globally conjugate. As an application, we
study the case where $\Gamma$ is the Weil group of a $p$-adic local field,
which is relevant to the recent approach to the local Langlands correspondence
for ${\rm G}_2$ and ${\rm PGSp}_6$ by Gan and Savin. As a second application,
we improve some result of Kret and Shin about ${\rm GSpin}_7$-valued Galois
representations.
