I tried to find the answer for this question, but I cannot find any helpful answers yet. I know extensions in Joomla 1.0 can work with Joomla 1.5 in Legacy mode, but I'm not sure in Joomla 1.6.
4 Answers
You cannot use a 1.5 extension on 1.6 without at least some minor modification. Depending on the extension, you might be able to update just the XML manifest and have a functioning extension. In other cases you may also have to rewrite some code if the extension makes use of depreciated code.
The Wiki page (in the official Joomla docs wiki) linked by Ram Kumar will give you all the info you need to upgrade an extension.

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We have needed some works to Convert ...!! here i had attached the link...!! I hope It will be help to you...!!! http://docs.joomla.org/Upgrading_a_Joomla_1.5_extension_to_Joomla_1.6

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A lot of changes has been put in Joomla 1.6. The components of Joomla 1.5 can't be used in Joomla 1.6 because of all the changes.
For more technical information see Joomla Wiki

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Unless you're a programmer,then the answer is no, they use a completely different structure, and for that matter you can't use a Joomla 1.5 extension on 1.7 also.
We often migrate extensions for some of our clients from 1.5 to 1.6 (and now 1.7), but it's a very painful process and takes some time (but it's feasible).

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