\version "2.12.3"

#(define (tuplet-number-to-beam tuplet-number)
  (let* ((tuplet-bracket (ly:grob-object tuplet-number 'bracket))
         (note-column (ly:grob-parent tuplet-number X))
         (stem (ly:grob-object note-column 'stem))
         (beam (ly:grob-object stem 'beam)))

     ;; Move (invisible) TupletBracket to beam, taking number with it
     (ly:grob-set-property! tuplet-bracket 'positions (ly:grob-property beam 'positions))))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\new PianoStaff <<
  \new Staff = "1" {
    s4
  }
  \new Staff = "2" {
    \relative c {
      \clef bass
      \override TupletNumber #'after-line-breaking = #tuplet-number-to-beam
      \times 2/3 {
        c8
        \change Staff = "1"
        c''
        \change Staff = "2"
        c,,
      }
    }
  }
>>