Can you send a transaction from non-native segwit to native(bech32) segwit address?
The wallet needs to be able to decode a bech32 address and construct the appropriate native witness output when sending funds. 

Given that your (hypothetical) wallet can spend P2SH(witness) outputs already, it is likely it can or will soon support native bech32 addresses, but there is no guarantee that the latter must be supported given the first.