It's really significant that he didn't tell you about giving it to her OP, and you only found out by seeing his phone.
Your partner has made multiple romantic gestures to another woman: roses and fossil. The first is a known romantic item, the second indicates that he has been thinking about her while away on a work trip (and has not been thinking about you in the same way). To me, the text you wrote up also suggests inappropriate closeness.
How is your relationship generally? Even if it's solid and he does lots of lovely thoughtful things for you all the time, he's still behaving inappropriately and you have good reason to be concerned.
Also: he knows exactly what he's doing and that it's wrong (which is why he hid it). Thoughtful effort with gifts is not something that most men engage in, sadly, even for close family/longstanding friends.
You'll have to speak to him about it, but this is a really sad situation. There's no getting around of the fact that he's making special gestures towards this woman. I couldn't live with whatever this means - whether it's just an ego thing for him (indicating a weakness of character), a lack of respect for you (he can stroke his ego and flirt with other women as he wishes), or - worst of all - shows he has strong feelings for this woman.
You know him best, and which of these things are likely.