Peter's basis would be exactly as you stated:
$151,256 (fair market value at date of death plus Peter's share of improvements made).
Sections 1014(a)(1) and 1016(a)(1).
Your basis would be the greater of what you pay Peter ($125,000) or Peter's adjusted basis at the time of the transfer ($151,256) so, obviously it would be the latter.
Section 1.1015-4(a)(1)
