The new couple are visiting the southeast Asian country of Cambodia for an exotic vacation that Hudson has been documenting on social media.
Earlier this week, Hudson shared an image taken from the country’s Phnom Kulen mountain range, writing, “It doesn’t take long to fall in love with the beautiful country of Cambodia.”
Later, she shared an image “wandering the market,” and another of she and Fujikawa’s local guide Vy.
Wrote Hudson, “Vy has taken us on the most insightful adventures and has shared with us in depth the tumultuous history of this country. He speaks of his personal hardships and those of his people, he shares stories of his starvation in his youth and the on going struggles of extreme poverty here.”
“He says that the great hope for him as a guide is to share with the world how beautiful and special it is here,” she added. “And boy is it beautiful! The culture, the landscape and mostly the people! Feeling lucky to have Vy. Vy we love you!!”
On Wednesday, Hudson shared a selfie with Vy and her boyfriend taken in what appeared to be a hut. Of the lush tropical setting, she told her followers, “Taking rest from the rain in the jungle.”
Hudson also teased a partnership with the World Food Programme, writing on Instagram, “Looking forward to sharing this experience with you. To be continued… @worldfoodprogramme_official #Cambodia.”
The World Food Programme helps combat hunger in impoverished countries and areas worldwide, according to the organization’s website.
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Hudson and the alt-rocker were first spotted out together in March, with an insider telling PEOPLE at the time, “Kate’s a free spirit who has always been attracted to musicians. But Danny also appeals to her because he is talented, bright and cosmopolitan like she is.”
Added the source at the time, “Kate’s enjoying herself. At this point it’s not serious.”