** Shares of Respiri RSH.AX rise as much as 7.5% to A$0.086

** e-health software services provider signs binding purchase agreement to buy U.S.-based connected care organisation Orb Health Inc for $9 mln

** Expects acquisition to generate synergies totalling ~A$3.5 mln ($2 mln) in the initial full 12 months of operations

** About 2.6 shares traded, 1.2x the 30-day avg

** RSH has more than doubled YTD

($1 = A$1.5492)

(Reporting by Sherin Sunny in Bengaluru)

((Sherin.Sunny@thomsonreuters.com))