** Shares of Respiri rise as much as 8.6% to A$0.038, their highest levels since Oct 3

** The e-health software services co enters into its first remote patient monitoring agreements with two of Hawaii's skilled nursing facilities, Liliha Healthcare Centre and Care Center of Honolulu, to help with transition of patients to home care

** Co says agreements to generate more than $1 mln p.a. from

~1,000 annual patient discharges

** About 2.2 mln shares change hands, 3.3 times the 30-day average volume of shares

** Stock has risen 16.7% this year, as of last close

(Reporting by Sherin Sunny in Bengaluru)

((Sherin.Sunny@thomsonreuters.com))