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In few simple words:
1) Uninstall JoomlaStats component in Joomla 1.0.15 using standard Joomla CMS uninstall method
(joomla backend -> menu -> Installers -> Components -> uninstall JoomlaStats component)
2) Migrate Joomla CMS 1.0.15 to Joomla CMS 1.5.12
3) Simply install main component (com_joomlastats_v2.3.1.zip) in Joomla CMS 1.5.12, and all Your statistics will be retained
4) Uninstall JoomlaStats component com_joomlastats_v2.3.1.zip in Joomla 1.5.12 using standard Joomla CMS uninstall method
(joomla backend -> menu -> Install/Uninstall -> Components -> uninstall JoomlaStats component)
5) Uninstall "bot_jstats_activate" it is obsolete and could cause "Restricted Access"
6) Install main component (com_joomlastats_v3.0.0.zip) in Joomla CMS 1.5.12, and all Your statistics will be retained
6) Now You can turn of Legacy mode in Joomla CMS v1.5.12
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