Linking batteries of different amp/hr ratings

[Isetech]

If I have an amp/hr lithium battery with a built in BMS and a 7 amp/hr lithium battery with a built in BMS, can I link these batteries together when the power switches off?

I am busy setting up a system which will trickle charge the 7 amp/hr battery and pushing 5 amps into an 18 amp/hr battery to fast charge the battery in 4 hours.

The plan is to fit a relay so that when the power drops the 2 batteries will connect together, will the big battery damage the little battery.

We do it all the time with lead acid batteries, it just tops up the small lead acid battery. I just need to make sure the same will happen with a lithium battery?

[Justloadit]

Probably, however there may be a high inrush current, which may trigger the over current protection of the battery being connected, and the BMS disabling the battery.

You can reduce the current by inserting a 0.1 Ohm 5W resistor in series with the battery to control the inrush current.
It will have minimal effect in normal operation