Let’s look at important things here –
Moon - Moon represents Mind, Emotions, Mother, Local Government, Peace of Mind, Home Environment, Water, Milk etc.
Punarvasu - It is a nakshatra of rehabilitation and recovery process. It is very closely connected with after-care medical activities. It can also be a nakshatra of counselling. For more information on Punarvasu Nakshatra, please check this - https://www.astrosaxena.com/punnaksh.
Gemini - As Punarvasu is part of Gemini, Gemini sign and its representations become important when any planet is in Punarvasu/Gemini. Gemini is the 3rd sign of zodiac belt, so it represents many things related with 3rd house of horoscope like, Communication Skills (either written, oral or even by sign language), Marketing, Business etc. It is a sign basically related with communications and business ideas. Gemini is divided into 2 and half nakshatra of Mrigashira, Ardra and Punarvasu. Gemini's lord is Mercury, which is significator of Communications.
Cancer - As Punarvasu is also a part of Cancer, Cancer sign and its representations become important when any planet is in Punarvasu/Cancer. Cancer is 4th sign of Zodiac Belt, hence it represents the things represented by 4th house like Mother, Mother's Care, Emotions, Taking Care of Others and Nourishment etc. Cancer is consisted of 2 and half Nakshatras namely Punarvasu, Pushyami and Ashlesha. Cancer's lord is Moon, which again represents almost same things which Cancer and 4th house represents.
Mercury - As Mercury rules Gemini, Mercury’s position and dignity is important to know about the overall functioning of any planet in Punarvasu/Gemini.
Moon - As Moon rules Cancer, Moon's position and dignity is important to know about the overall functioning of any planet in Punarvasu/Cancer.
Jupiter - As Punarvasu is ruled by Jupiter, Jupiter's position and dignity will also have an important role in functioning and results of any planet in Punarvasu.
Houses Involved – Also, we can’t afford to forget the houses involved as a planet can be ruling different houses and sitting in different house for every person as per ascendant and planet’s position. To know overall affect, we have to consider the houses involved as those areas of life are being impacted.
Interpretation of Moon in Punarvasu Nakshatra – Now, when Moon is in Punarvasu Nakshatra which is coming after Ardra, we are moving a step ahead of the turmoil and chaotic events. It means this nakshatra represents people who take care of those who have suffered a turmoil. They provide them rehabilitation and kind of hope for the future. As Moon's basic nature is also about taking care and nourishing others, it certainly fits in to Punarvasu Nakshatra. The fact that it is ruled by Moon's best friend Jupiter also helps. But as it spreads from Gemini to Cancer, the end result can change as per the nature of sign involved. If Moon is in Punarvasu/Gemini, it shows that someone is trying to help, heal or rehabilitate others through his communications. So, it can be more like a counselor, guide, teacher or a coach etc. But in Cancer portion of Punarvasu which is a sign of taking care and nourishing others, they can be seen as healer, medical experts, care giver. So in both signs, person is helping someone in rehabilitation but in Gemini, it is through communication and in Cancer, it can be through actual healing or health care activities. Another difference can be that in Gemini section, they can be more clever and smart with business acumen but in Cancer section they can be more emotional and sensitive. Overall, good position to be a healer.
Role of Mercury – Mercury's position will become important in functioning and results of Moon in Punarvasu/Gemini as Mercury rules Gemini. If Mercury is in good dignity then Moon will have proper direction about the direction of his path or career.
Role of Moon – As we are trying to interpret Moon only in Punarvasu, we need not to see Moon's position separately.
Role of Jupiter - Likewise, Jupiter's placement is important to guide Moon in right direction, being Punarvasu's lord.
Other Factors – And of course, we need to consider conjunction, aspects, house lordship, house position and dashas etc to know the exact results of Moon in Punarvasu. So, we always need to take a holistic view of chart rather than just 1 planetary position.
Conclusion – So, this is how I see Moon in Punarvasu can work in a chart.