The fact that the mean and variance were sufficient statistics for a univariate normal distribution truncated at a fixed point was known to Fisher by 1931 . Hotelling  has recently observed the corresponding fact for the truncated multivariate normal distribution. It is the aim of this note to point out that these are special cases of a general result, namely: If a family of distributions admits a set of sufficient statistics, then the family obtained by truncation to a fixed set, or by fixed selection, also admits the SAME set of sufficient statistics.
"Sufficiency, Truncation and Selection." Ann. Math. Statist. 20 (2) 309 - 311, June, 1949. https://doi.org/10.1214/aoms/1177730042