Following examples, I tried to add processing of offline messages.
Structure of my system is:
SIP client <->Kamailio<->Asterisk<->Kamailio<->SIP client
Where Kamailio in above is same server, but SIP clients are different.
Now I have no problems with audio, video calls and messages, if both clients are online.
All messages received from client are sent to Asterisk, where I can or not process them and then I forward back to Kamailio. When messages came from Asterisk server, then they are sent directly to end user.
Sending messages to end user - I call this function, only if message come from allow_source_address():
route[MSILO_MESSAGE]{
if (lookup("location")){
xlog(" Relying");
t_relay();
}else{
xlog("Storing MSILO_MESSAGE $ru-$tu-$ou");
m_store("$ru");
t_relay();
t_reply("202", "Accepted");
};
exit();
}
When client register: 
route[REGISTRAR] {
if (is_method("REGISTER"))
{
if(isflagset(FLT_NATS))
{
setbflag(FLB_NATB);
# uncomment next line to do SIP NAT pinging 
## setbflag(FLB_NATSIPPING);
}
if (!save("location",0x04))
sl_reply_error();
# MSILO - dumping user's offline messages
if (m_dump("$fu")){
xlog("MSILO: offline messages for $fu dumped - if they were  \n");
}else{
xlog("MSILO: no offline messages dumped\n");
};
exit;
}
}
I am sending message to offline contact, and I see record in silo table. Record looks perfect.
Then offline contact become online, I see in debug MSILO: offline messages for {offlined contact} dumped - if they were  
But client do not receive nothing.
In case all contacts are online, then message go to contact, and is not stored in silo.
Setup of msilio is:
loadmodule "msilo.so"

modparam("msilo","db_url",DBURL)
modparam("msilo","from_address","sip:registrar@MY DOMAIN")
modparam("msilo","contact_hdr","Contact: registrar@MY DOMAIN:5060;msilo=yes\r\n")
modparam("msilo","content_type_hdr","Content-Type: text/plain\r\n")
modparam("msilo","offline_message","***$rU***$rb***")
By the way - I receive in Asterisk offline message.
Obviously, I am doing something wrong, but I cant understand what.
Any help is welcome.
Version of Kamailio is:
#~> kamailio -V
version: kamailio 3.2.3 (x86_64/linux) 59f87e
flags: STATS: Off, USE_IPV6, USE_TCP, USE_TLS, TLS_HOOKS, USE_RAW_SOCKS, DISABLE_NAGLE, USE_MCAST, DNS_IP_HACK, SHM_MEM, SHM_MMAP, PKG_MALLOC, DBG_QM_MALLOC, USE_FUTEX, FAST_LOCK-ADAPTIVE_WAIT, USE_DNS_CACHE, USE_DNS_FAILOVER, USE_NAPTR, USE_DST_BLACKLIST, HAVE_RESOLV_RES
ADAPTIVE_WAIT_LOOPS=1024, MAX_RECV_BUFFER_SIZE 262144, MAX_LISTEN 16, MAX_URI_SIZE 1024, BUF_SIZE 65535, DEFAULT PKG_SIZE 4MB
poll method support: poll, epoll_lt, epoll_et, sigio_rt, select.
id: 59f87e 
compiled on 14:43:47 Jul 19 2012 with gcc 4.5.2