Before revision:  A necessary condition is derived from envelope theorem, which explicitly formulates the state-dependent payment rules in terms of allocation rules. A class of monotone environment is considered to characterize the optimal stopping by a threshold rule. The posted-price payment rules are then pinned down  in terms of the allocation rule and the threshold function up to a constant.
After revision:  The payment rules are then pinned down in terms of the allocation rule and the threshold function up to a constant.