Yes, as per the direct words of one of the most pious woman - Devī Anasūyā, the chaste wife of Mahaṛṣi Atri, the wife accrues half the merit of her husband's peity.
Devī Anasūyā says these words as advice to the wife of the leprosy ridden Kauśika brāhmiṇa, who stopped the sun-rise owing to a curse from the Māṇḍavya ṛṣi.
तस्मात् साध्वि ! महाभागे ! पतिशुश्रूषणं प्रति ।
त्वया मतिः सदा
कार्या यतो भर्ता परा गतिः ॥१६.६२॥
यद्देवेभ्यो यच्च पित्रागतेभ्यः
कुर्याद्भर्ताभ्यर्च्चनं सत्क्रियातः ।
तस्याप्यर्धं केवलानन्यचित्ता
नारी भुङ्क्ते भर्तृशुश्रूषयैव ॥१६.६३॥
- 62,63. Therefore, O virtuous and exalted lady, let thy mind ever be turned
towards obedience to thy husband, since a husband is a wife's supreme
bliss. Whatever worship the husband may offer by right ceremonies to
the gods, and whatever to the pitṛs and guests, even one half of that
does the wife, whose mind is centred on him alone, enjoy by very
obedience to her husband.”
English Translation by Frederick Eden Pargiter
One may access the Sanskrit + Hindi Translation of the above excerpt from here or the abridged Gita Press Gorakhpur version from here.
To conclude:
If married person does any charity from "His own earned income" (not from income of wife or forefathers), then half of his Punnya is given to his wife and half to him.
Answer - Yes, the wife is given half the merit of her husband's peity, provided she is chaste and devoted to her husband.
But if he is un-married then full Punnya goes in his account. Is it true?
In general for an average person, the acts of peity like Yajña, charity, donations, etc. are to be practised in the Gṛhastha-āśrama only, and by default Gṛhastha will have a wife.
In fact, in this official video from the Puri Math, by Govardhan-Puri Math Shankaracharya, Swami Nischalananda ji.
Wife gets half the fruits of husband's peity (good karmas), while husband gets no half from the wife's peity.
Husband gets half the sin of the wife's sinful acts, while wife does not accumulates any bad karmic fruit from sinful activities of her husband.
In general, a person (especially a man) must be married (Gṛhastha). Nischalananda ji cites the
case of god Sri Râma and the golden Statue of goddess Sitâ he made to
perform the Yajña.
However, when unmarried, it will be more probable that the person is solely responsible for his own karmas, provided they're above the age of 14 as set by Māṇḍavya ṛṣi.