 Floating-rate payment bond replication

Buy one maturity-$(T-1)$ bond and short $1+f$ maturity-$T$ bonds. Reinvest the first bond's unit maturity payoff in $1/P_{T-1}(T)$ maturity-$T$ bonds. This self-financing portfolio pays $r_T-f$ at $T$. The replication uses only the adjacent maturities and does not require completeness of the whole bond market.