  Contributions to HFS and to the Lamb shift intervals of order
$\alpha^2(Z\alpha)^5$ induced by the graph with the two-loop overlapping
electron self-energy diagram inserted in the electron line are considered.
Explicit expression for the overlapping two-loop self-energy diagram in the
Fried-Yennie gauge is obtained. Contributions both to HFS and Lamb shift
induced by the diagram containing such subgraph are calculated.
