Assalamo Alaikum w W
Question: Is it permissible to wish on wedding anniversary between husband and wife only.and to give gift.
Jazakallahu Khairun

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Wa ‘Alaykum as-Salaam wa Rahmatullah,

Islam encourages giving gifts to one another. The Prophet (May Allah bless him and give him peace) has mentioned:
تهادوا تحابوا
‘Give gifts to one another as this will increase the love amongst you.’

 In the relationship between a husband and wife, occasional gifts are even more emphasised, as it is absolutely necessary for the husband and wife to love one another. 

However, at the same time, Islam discourages imitating and being copycats. 
Celebrating an anniversary is a mere formality. Therfore avoid it.

It is better to exchange gifts on a regular basis to strengthen the relationship, rather than restricting it to one day of the year.