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I have a PP3 Ni-Mh rechargable 9v
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There is no such thing. Rechargeable PP3's are a nightmare area as you will find two quite different kinds. I have encountered 7.2V and 8.4V ones which present as PP3's - the idea is that a freshly charged one might be similar to a flatish real one. Try using a real PP3 and see if it makes a difference.
Likewise a Li cell is a poor approximation to a pair of regular cells.