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For asymptotically flat spacetimes, a conjecture by Strominger states thatasymptotic BMS-supertranslations and their associated charges at past nullinfinity $\mathscr{I}^{-}$ can be related to those at future null infinity$\mathscr{I}^{+}$ via an antipodal map at spatial infinity $i^{0}$. We analysethe validity of this conjecture using Friedrich's formulation of spatialinfinity, which gives rise to a regular initial value problem for the conformalfield equations at spatial infinity. A central structure in this analysis isthe cylinder at spatial infinity representing a blow-up of the standard spatialinfinity point $i^{0}$ to a 2-sphere. The cylinder touches past and future nullinfinities $\mathscr{I}^{\pm}$ at the critical sets. We show that for a genericclass of asymptotically Euclidean and regular initial data,BMS-supertranslation charges are not well-defined at the critical sets unlessthe initial data satisfies an extra regularity condition. We also show thatgiven initial data that satisfy the regularity condition, BMS-supertranslationcharges at the critical sets are fully determined by the initial data and thatthe relation between the charges at past null infinity and those at future nullinfinity directly follows from our regularity condition.

BMS-supertranslation charges at the critical sets of null infinity