autodiscover from another domain

I believe you have forest / domain trust and have linked mailboxes

You can create domain.com dns zone (SMTP domain) on your DNS server and create autodiscover host(A) record pointing to exchange CAS server FQDN (may be you have NLB FQDN)

Because domain joined corporate outlook clients 1st try to locate SCP in AD which is not available in non exchange domains and hence autodiscover will try to resolve exchange server with autodiscover record
The last alternative could be you can create SRV record for autodiscover in your DNS pointing to CAS server in exchange domain

since now I have no domain trust.

Still autodiscover record should help you to locate exchange server and configure outlook (outlook anywhere)

do I need a trust or is it possible without ?

for outlook anywhere to work no trust is required

outlook anywhere is protocol run on rpc over https directly from internet

outlook can be configured as long as autodiscover.domain.com is accessible to clients either from internet / intranet where domain.com is your SMTP domain

ok and when I not use outlook anywhere , then a trust is needed ?
A two way trust or a one way trust is enough ?
Which direction ?

My situation is ...

The exchange in domain K  will be removed.
All mailboxes needs to be moved to my smtp domain , domain H .
In the end I have just one exchange server for two different domains.

Are these linked mailboxes ?
Or what kind of scenario is this called ?
I also need autodiscover, do I need a trust in this case ?

Thanks a lot , I will look for it.