I want to disprove false allegation against me in heinous crime, and eventually I fond a lawyer who agreed to help me in some way. However, it turned out that in past the lawyer defended my accuser in some charges.
That is not an effective assistance issue, it is a conflict issue. It might or might not be a serious problem both technically and in practice. There is not enough information in your posting to say for sure.
Divorce / Separation Lawyer
You should probably find another lawyer. This lawyer may have a conflict of interest.
Criminal Defense Attorney
Even though the prior attorney may have excellent legal ability and composition to defend your case, the present situation calls for a completely remote and impartial attorney who did not represent your "prior accuser in a different matter," as you stated. Such internal conflict must be avoided at all costs. Research and select a reputable criminal counsel of your choice, as this jurisdiction has many splendid counsels.
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Criminal Defense Attorney
This is clearly a conflict of interest. I question whether the lawyer you found would even agree to represent you. In any event, you should find another attorney who does not have this conflict.
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